I was told I should make this its own thread after I posted in the general discussion, so I will. As I did with Aftershock Tremor in MKX, here are my Cap matchup notes! Please let me know if anything seems wrong, because I want to make this truly useful. Also, I know these won't work in every situation due to stones and tagging, but there are times when they'll help.
Backflip goes through all projectiles except Daggers and Lances, but he’ll need to delay the timing of the second/third Daggers and second Lance to punish your move.
-Daggers and Lances will beat out Shield Slash L, as well as both Trick Shields. He can also jump over Shield Slash L and punish with a projectile.
-Charging Star H will blow through all ground projectiles and hit him. Although he can super-cancel, you can too, so this is a serious meta situation.
-Stars & Stripes renders his instant J.hk (if you can read it) useless.
-Shield Deflect from not quite 2/3 screen distance or closer will stuff Charging Star H. This will even work if you super-cancel, so don’t just throw this move out.
Chain of Hunting L, H, L and H, H, L strings have gaps between the second and third hits that can be punished with Stars & Stripes L (he’s in the air during the second hit, so you’ll know which ones). This also applies to L, H, H (not as big of a gap, though, so you’ll need to reversal).
-Reversal Stars & Stripes L after a blocked ground Predator Arts will hit him during the second hit’s startup and before he gets far enough away.
-Ground Shield Slash H can shut down ground Wall Jump rather conveniently from halfscreen or further if you do it right after he bounces off the ground. Stars & Stripes L will deal with it any closer. Stars & Stripes H can deal with the air version right before he “touches” (for lack of a batter word) you.
-Stars & Stripes H can be done during the gap between the second and third hits of Hazard Zone to stuff it (L version will whiff due to the range you’re pushed to).
-Stars & Stripes H will stuff Sudden Death (downward air claw super).
-Air Shield Slash L will stuff or trade with Air Interceptor.
Liberty Shock nullifies Photon Blast. Watch for super-canceling, though.
-Photon Blast easily beats out both shield throws, so there’s really no point in using them in this matchup.
-A blocked Blitz Blow can easily be punished with reversal Stars & Stripes H.
-Strike Flurry is full combo punishable on block, but make sure to use S.lk x2, as its crouching counterpart doesn’t have as much range and won’t convert.
-Don’t use Liberty Shock when Photon Absorber is active, because her armor will absorb your counter and she’ll be able to punish with a full combo. If she decides to activate it after a blockstring or raw in front of you, Charging Star H (reversal if blocking) will ignore her armor and hit her.
-If you predict she’ll do Takeoff (command grab), which hits from two character spaces away, backdash and cancel it with Charging Star H.
Trick Shield L will go beneath Flamethrower.
-Leap Kick high-profiles him when he’s in Prone Position and crosses him up. Shoulder Tackle from this stance will stuff your move, though, so only do this if he fires off a shot and you’re close enough.
-Shotgun will stuff all shield throws, but Liberty Shock L from halfscreen or closer deals with this move. You can also Backflip through the shot from this range and end up in front of him.
-Machine Gun will beat out Shield Slash L, but your move will absorb all of his bullets and allow you to act a split-second before his move ends. Also, Trick Shield H from halfscreen or closer will high-profile the shots and hit him.
-If he runs out of Magnum ammo and reloads raw, Charging Star H from 2/3 screen distance or closer will punish him.
-You can’t backflip through Land Mine.
-If he’s cornered you and you block Combination Punch L and its two following punches, you can Stars & Stripes L through the gap between the punches and Magnum. Midscreen, you can only punish it if he needs to reload with Charging Star L; Stars & Stripes will whiff and other options won’t be fast enough. Combination Punch H’s string ender (shotgun) has a gap that Charging Star H can go through at all ranges.
Stars & Stripes L easily beats out Kakukyakuraku (halfscreen air flip).
-Shield throws beat out Lightning Legs on both the ground and in the air. Stars & Stripes easily beats out air Legs, as well. These apply to Spinning Bird Kick, also.
-Liberty Shock H needs to be used against Spinning Bird Kick due to her being airborne.
-Kikoken (fireball) and shield throws will beat each other out.
-Shield throws should not be done from halfscreen or closer when she has meter and isn’t doing anything due to Hoyokusen.
Liberty Shock L will stuff Stinger from 2/3 screen distance or closer. Stars & Stripes L or Liberty Shock L during the gap in Million Stabs followup between the constant stabs and ending one will stuff it. Concerning Million Stabs’ cancels:
Drive (wave projectile) can be Backflipped through.
Stars & Stripes L will punish Air Trick (teleporting above).
Liberty Shock L during Volcano/Beehive’s gap between the kicks and stomp will stuff it.
-Stars & Stripes will stuff Helm Breaker, but only at close-range. Any further and your move will just whiff or be stuffed.
-Rain Storm (air downward bullets) can be stuffed with Stars & Stripes H if he does it when jumping over you (at normal and super jump heights, but not super + double jump height).
-Scatter Shot (guns) will beat out Shield Slash L and Trick Shield L, and Liberty Shock won’t work against it. From two steps further than halfscreen (not quite 2/3 screen distance) or farther, Trick Shield H will high-profile Scatter Shot and hit him (hold back during your descent to block the shots). Done any closer, though, and you’ll either be hit by the bullets or Prop Shredder followup.
-Reversal Stars & Stripes L right after a blocked Crystal will stuff Revolver followup. Reversal Charging Star L will stuff Million Carats followup to Revolver (you’ll be frozen if you do Stars & Stripes).
-Liberty Shock L right as he does Jet Stream (elemental blade charge) from anywhere onscreen will stuff his move. Of course, you could always just block and punish it with a combo.
-Liberty Shock H and Stars & Stripes will beat out The Hammer and Sky Dance.
-The ending energy shot of Million Dollars can be Backflipped through right before it hits you. Done too early, though, and you’ll be hit.
S/C.lk x2 is what you’ll want to use up-close due to Illusion, but the trick is to delay the second hit a bit late; if he does the counter and ends up behind you, the second kick will hit him and allow you to combo.
-Flames of the Faltine, Dagger of Denak, and Mystic Sword Shockwave L can be Backflipped through. You’ll only go through the first of the H Daggers and be hit by the other two, though. You can’t Backflip through Eye of Agamotto because it will follow your attack (due to homing) and hit you. You can Backflip through Tear of Agamotto and avoid the explosion.
-Liberty Shock L can be used two consecutive times against Bolts of Balthakk. Watch for super-canceling, though.
-A blocked Mystic Sword Duel Slash H has a gap between the third and final hits that Stars & Stripes L will go through.
-When he has the three Graces of Hoggoth in the large red triangular formation and you’re fullscreen, Charging Star H will go through the flame as it’s halfway to the third Grace (same with the red scattered ground formation). If they’re in the small orange triangular formation above you, Backflipping a split-second after the flame goes through the second Grace will avoid the crossup beam (same applies to large orange triangular formation).
Dark Matter can be Backflipped through right before it hits you. If you do it too early, you’ll get hit.
-Both versions of Charging Star will go through Flame Carpet if done at halfscreen or closer. If done any further, you’ll be hit.
-Dark Hole stops your shield throws, so using them is pointless here.
-You can stuff the startup of Dark Hole (all versions; he folds his arms) with Charging Star from halfscreen or closer. Same with Purification (he raises his arm). Despite being able to super-cancel the moves, he will most likely be hit or you’ll trade.
-Charging Star H right before Stalking Flare hits you will go right through it. Done too early, though, and you’ll be hit.
-Both versions of Mass Change can be dealt with via Stars & Stripes H (L versions whiffs against his L version).
Hell Spitfire can be Backflipped through right before it hits you. Do it too late, though, and you’ll be hit.
-Neither Backflip nor Charging Star will go through Tornado, and it will absorb shield throws. Trick Shield H right in front of the Tornado has a chance to stop him from advancing behind it, though.
-Hell’s Elevator will allow him to avoid ground/low attacks, but if you can read it (either version), Stars & Stripes will stuff it before he can do anything else.
-Demon Missile Lp/Hp/Hk will get beaten out by Shield Slash L. Leap Kick can stuff charged Lp version if you do it about a full second after he starts charging (too late and you’ll be hit, though).
Liberty Shock L works against raw Snapshot and Shot Timer (camera on tripod).
You can Backflip through zombies right before they hit you. Too early, though, and they’ll grab you.
Liberty Shock L will not work against Blue Light Special due to the cart absorbing your counter. You also can’t Backflip through this move.
Trick Shield L will low-profile Object Throw.
-Lv.2: Raw Roundhouse Kick is rather easy to Backflip through due to its startup and active frames.
Barrel Roll is basically the same move as your Backflip, so be mindful of this.
-Lv.3: Tools of Survival reaches slightly less than halfscreen and can be dealt with via Liberty Shock from this range or closer.
Don’t do Trick Shield H or raw Leap Kick due to Funny Face Crusher.
Shield Slash L will stuff ground Outside the Box (Servbot head charge; it goes through Trick Shield L), while H version will stuff his air version (goes through Trick Shield H).
-Lv.4+5: Liberty Shock L from halfscreen or closer will stuff Tools of Survival. Any further will whiff and you’ll be hit, though. The same applies to This Looks Useful.
H Shoot & Slash will beat out Shield Slash if done at the same time, so don’t get predictable. Also beats out Liberty Shock from long-range.
-Charging Star H will either beat out or trade with H Shoot & Slash from halfscreen (must be done during her startup).
-Concerning followups to H Shoot & Slash:
Godslayer followup is not safe on block from any range. If she does it from max range, punish with Charging Star H or super.
Stars and Stripes conveniently deals with both Arch Shot followups. Use L or H version in response to her doing the same.
Divine Slide followup can only be punished with Charging Star H since she gets pushed away quite a bit.
-Quickly input Starts & Stripes L after the third hit of a blocked Slash Rush to blow right through it.
-Holding up-back during the startup of raw Celestial Barrage from any range (if you’re not doing anything) will either block or avoid it. If she does it close, full combo punish when you land.
Although Liberty Shock can absorb Rage Whip from a distance, he can cancel into Chain of Rebuttal to put you in blockstun and push you away, giving him the desired space. Only use the move at close-range.
-From 2/3 screen distance, if you can get a read on Wraith Whip (low chain), Trick Shield H will high-profile it and hit him as he stands up (or make him block).
-Liberty Shock H conveniently deals with Damnation Whip (air downward chain).
-Leap Kick high-profiles Hellfire L from all ranges (that it hits), allowing for a full combo punish. Watch for super-canceling, though.
-Stars & Stripes L during the gap between a blocked Seventh Circle Punishment and either of its followups will beat it out.
Liberty Shock L from halfscreen or closer can stop ground Steel Pipe and allow you to combo.
-Shield Slash L will stuff Violent Axe, but lose to Hoodlum Launcher (Backflip can deal with this move easily).
-Liberty Shock loses to Double Lariat due to his invincibility, and Backflip won’t go through it. The best thing to do if you suspect this move is backdash and Shield Slash L, which will allow you to combo if he lets it rip. This is also a good way to deal with Flying Piledriver.
-Both versions of Trick Shield can effectively deal with Cleanin’ up the City (barrel), since the H version goes behind him and the L version beneath and they don’t touch the barrel (the barrel will absorb L version from fullscreen).
-Liberty Shock L during the gap between the punches and last hit of Rapid Fire Fist will stun him and allow you to combo.
-Stars & Stripes H will stuff Giant Haggar Press.
Quick Shot Greyhound will stuff Shield Slash L and hit you. Trick Shield L, however, can low-profile this move if done right when he releases the arrows. These also apply to Spritzer.
-Considering Trick Maneuver and its followups (L meaning roll and H meaning jump):
Trick Shield H can high-profile Violet Fizz L (poison), while H version can be stuffed with Shield Slash H.
Trick Shield L will destroy both versions of Jack Rose (explosive).
Leap Kick can high-profile Icebreaker L, while you can easily Backflip through H version (when it stays on the ground).
Charging Star H will go through both versions of Scorpion (upward electric) before it hits the ground.
-Repeatedly tapping the buttons for Backflip during the startup of raw Gimlet will go through it. Since normals can be canceled into Backflip, this is a good way to bait him into wasting meter.
Liberty Shock doesn’t work against charged Impact Punch due to its armor. The same applies to Gamma Charge.
-Gamma Wave stuffs all shield throws, so don’t use them when he’s not doing anything.
-He will most likely follow up a blocked Gamma Charge with Gamma Air Charge, then A.lk on his way down. Stars & Stripes H stuffs his normal conveniently.
-If you can read Gamma Tornado, Backflip to go through it and punish him from the other side with Leap Kick-started combo.
-Liberty Shock H against Gamma Crush as he comes down will protect you and allow you to punish him during his recovery.
Trick Shield H from 2/3 screen distance or closer will high-profile Arm Missile.
-Unibeam will easily destroy shield throws. Liberty Shock L works well against it, because even though he can super-cancel, you’ll recover before Proton Cannon can hit you.
-Never do raw Liberty Shock L any further than one step closer than halfscreen due to Repulsor Ray; the counter won’t hit that far and his followup rays will punish you.
-Raw ground Smart Mine can be stuffed anywhere on screen; from halfscreen or further, use Shield Slash H, and from 1/3 screen distance or closer, use Stars & Stripes L. Air version can be destroyed by Shield Slash H, but Stars & Stripes will lose to it.
-If you can read Proton Cannon from halfscreen or further, Trick Shield L will stuff it. Any closer, and it can be stuffed with Liberty Shock L.
Although you won’t be able to use ground Shield Slash or Trick Shield due to his super, Liberty Shock will work against it if you get a read (not after his super’s startup, though) and keep you safe, while he’ll have wasted a bar.
-Overall, shield throws are almost pointless to use in this matchup, since almost all of his specials deal with them conveniently.
-Liberty Shock against L Sangue Sacrificale (spinner) when you’re close to him will hit him. However, if you’re any further, you’ll simply be hit after your counter and not reach him.
-Liberty Shock beats out Falce Inizio (scythe) from halfscreen or closer. Also beats out Spirale Divina (claw grab) from 1/3 screen distance or closer.
-Stars & Stripes conveniently beats out Falce Primordiale (air-to-ground grab) and Turbine dell’Ira (downward air drill).
Liberty Shock L will work against Circle Slash from halfscreen or closer and Lunging Strike from not quite 2/3 screen distance or closer.
-Liberty Shock L will not work against Overhead Slash due to armor, but Charging Star can stuff it. This also applies to Draw Slash L (H version’s armor will not be stuffed).
-Trick Shield L will stuff Dodge from halfscreen or further; if it doesn’t hit her during the roll, it has a chance to hit her on its way back to you.
-Arrow Strike will go through shield throws and hit you. You also can’t backflip through them due to multiple hits.
-Demolisher Demon Dance has a gap before the last hit (when she slams her sword on the ground) that Stars & Stripes H can punish (L version whiffs).
Stars & Stripes easily beats out Shell Kick.
-Soul Fist and shield throws will destroy each other. Charging Star and Backflip (if done right before it hits you) go through Soul Fist, but you must be mindful of super-canceling into Shadow Servant, which will punish you hard.
-Shield Slash H will destroy L Harmonious Spear “balls” from anywhere on screen, while Stars & Stripes L will destroy the H version when it’s above you.
-Charging Star H against Finishing Shower from midscreen or closer will trade in your favor damage-wise.
If you can read Deadly Reach, Trick Shield L will low-profile the attack and hit him.
-Don’t attempt to use Liberty Shock against Clothesline Rocket or Launcher Slam due to armor. Stars & Stripes L will stuff them, though.
-You can backflip through his rockets right before they hit you, but don’t do it too early or you’ll be hit.
-Liberty Shock during the gap between the fourth and fifth hits of Biohazard Rush will counter and let you combo.
-Do Stars & Stripes H when he comes down during Bioweapon Assault to stuff his attack.
Leap Kick will beat out Nova Slam during its startup. Done too late, though, and you’ll be hit.
-Trick Shield L is very useful in this matchup, since it will prevent him from doing Shooting Punch, ground Nova Strike L, and Centurion Rush L and stuff the moves. He won’t be able to super-cancel in time before the shield hits, as well.
-If he does Energy Javelin from halfscreen or closer, Charging Star H will stuff the move. If he super-cancels, your move will stuff Gravimetric Blaster but lose to or trade with Super Nova.
-Stars & Stripes L easily stuffs Centurion Rush H.
Shield Slash L will go over Spitfire + Twice and hit him before his projectiles hit you. If done from fullscreen, you’ll be able to block before his shots hit you. Also applies to Spitspark.
-Groot Slam will absorb shield throws. Trick Shield H from halfscreen or closer during his startup will cause the Shield to go behind Groot and hit Rocket.
-Trick Shield L will destroy ground traps. You can also Backflip through them.
-Against a blocked Rock ‘n’ Roll, Charging Star H during the gap between the bullets and energy shot from halfscreen will stuff it, while you can dash and then Backflip during the gap from any further to combo punish.
Shield Slash L and Hadouken will destroy each other. Be careful when he has meter, though, because super-canceling will punish you.
-If he starts charging Sen Hadouken (beam) when you’re 2/3 screen distance or closer, Charging Star H will stuff it if you’re fast enough.
-Like your DP, his is invincible, as well, so don’t attack him from the air.
-You’ll want to use Liberty Shock H to deal with Tatsu, since he’s airborne during the move.
-Stars & Stripes easily beats out air Tatsu.
Trick Shield H will high-profile Overload Laser from 2/3 screen distance or closer.
-Liberty Shock L will stuff all versions of Arc Divide (except HP because it’s an anti-air) from halfscreen or closer. Nothing of yours will destroy or go through “slashes”.
-Shield Slash L and Reflector Magnum (rockets) will destroy each other.
-A normal canceled into Stars & Stripes H is a good way to deal with Counter Teleport: your DP will hit him right as he appears. S/C.lk is probably the best for this, but a slower normal like S.hk can really bait him into doing it, as well.
-Doom Buster can be Backflipped through right before it hit you. Too early, though, and you’ll be hit.
-Reversal Liberty Shock L during the gap after the first hit of Rave Divide will stuff his super.
Liberty Shock L will conveniently beat out Right Hook (overhead) from 2/3 screen distance or further. He cannot cancel this move.
-You can Backflip through Wire Grapple L right before the claw hits you. Too early or late, though, and he will catch you. Trick Shield H can high-profile this move and hit him from 2/3 screen distance or closer.
-Leap Kick will high-profile Jaw Breaker L (command grab) and allow you to combo punish. H version can catch you, though.
-Each blocked Zip Line has a gap that you can do Stars & Stripes L through.
-Stars & Stripes conveniently stuffs Bionic Bomber (air-to-ground slam).
-Shield Throws will destroy Hand Grenade.
-Whiffed normals canceled into Backflip can effectively bait him into doing Bionic Lancer; repeatedly tap the input during his super’s startup to go through it.
Web Ball and shield throws will destroy each other.
-Starts & Stripes L during the gap between a blocked Spider Sting L and Bite followup will beat it out.
-Liberty Shock H will beat out Web Swing from all ranges; either that, or you’ll low-profile it (lol).
-Ground Shield Slash H will stuff Maximum Spider.
-Liberty Shock L stuffs Web Throw.
-Charging Star H beats out both versions of Spider Canon if done during his startup.
Stars & Stripes conveniently stuffs Hk Vajra. Must be done on his way down, though, or else he’ll hit you. The same applies to Liberty Shock H.
-Stars & Stripes L done right as he jumps in front of you can stuff Excalibur lp/lk.
-H Gram will either stuff Shield Slash L or trade with it. Trick Shield H can high-profile H Gram and hit him from 2/3 screen distance or closer.
-Charging Star H during Wall Cling will avoid or hit all of his followups.
Trick Shield H from halfscreen will high-profile Titan’s Gaze and force him to block after recovery or get hit. Also a good way to deal with Insurrection’s End (command grab; closer).
-Palm Breaker does not work against either version of Shield Slash on the ground or airborne, and he will get hit.
-Liberty Shock does not work against Titan Charge L because of the armor, but it does work against H version.
-Trick Shield L will go underneath Titan’s Shield L from all ranges except close-range.
-Liberty Shock conveniently deals with Emperor’s Stance.
-Stars & Stripes H deals with both versions of Titan’s Deceit. L version whiffs against both.
Spinning Thunder will stuff shield throws on the ground.
-Don’t try to backflip through Mighty Spark Mjolnir, because the returning hammer will hit you before you recover. Although Charging Star H can go through it at the right range, the timing is rather impractical.
-Stars & Stripes will beat out a fully charged Mighty Smash.
-Don’t try to anti-air a fully charged Mighty Strike, because you’ll get beaten out due to its armor and multi-hits.
-If you can read Mighty Blow (it has a good amount of startup), backflip to avoid it and punish with Leap Kick-started combo. Don’t just Backflip for no reason, though, because he can easily catch you with Mighty Hurricane.
Death Ray can conveniently be dealt with via Liberty Shock. Watch for super-canceling, though.
-Liberty Shock easily deals with both versions of Protonium Emitter whether he does it raw or cancels from a string (it does not combo).
-After a blocked Melt Blast, he hovers before being able to do anything else, so punish with Stars & Stripes H.
-If he calls a drone after a blockstring, reversal Charging Star L will hit him and stop the drone.
-Liberty Shock H easily deals with Air Smash Drone (assuming he’s not close when he does it).
Shield Slash L and all versions of X Buster will destroy each other.
-Concerning X Buster’s followups:
Dash can be dealt with via Liberty Shock L from slightly less than halfscreen or closer, because despite your counter working against the projectile, he’ll be right behind it and be stunned for a combo. This also applies to Slide.
Buster Hammer can be stuffed by Stars & Stripes L from halfscreen or closer; do it right before the projectile hits you to go through it and hit him. Done any earlier, though, and he’ll hit you.
If you can read Backstep, Backflip immediately as he lets go of his shot to go through it and combo punish him before he recovers.
-Backflip right as you hear the icy (for lack of a better word) noise when Frost Shield is in the air to avoid it.
-Reversal Backflip after a blocked Boomerang Cutter will avoid the returning hit and stuff whatever he does next with C.lk x2.
Hyper Zero Blaster at all levels and Shield Slash L will destroy each other.
-Stars & Stripes L will hit ground and air Hienkyaku (dash) regardless of what side of you he’s on during the move.
-If Hyper Zero Blaster is charged and he does a blocked or whiffed Ryuenjin (DP), Stars & Stripes L will stuff the followup Hyouretsuzan (ice sword slam).
-Stars & Stripes L will beat out Sentsuizan (air downward slash).
-Liberty Shock L done right as he lands from Raikousen (lightning dash) will absorb it regardless of the side he lands on. Does not work when Sougenmu is active.
-You can backflip through Genmu Zero (lol).