Neon Genesis Evangelion, in Episode 9, features the angel Israfel, which splits into two and can only be defeated by two pilots using an identical sequence of simultaneous attacks. By way of dance. In fact, this trope encapsulates the episode: Shinji and Asuka's arguments with each other, their attempts to synchronize their everyday lives, and their final dance number all typify it.
Not to mention the fight between EVA-01 and EVA-02 in Episode 24.
Cardcaptor Sakura does much the same with the Twin card, which can only be defeated by two allies using an identical sequence of simultaneous attacks. But with martial arts this time.
Any fight between the two Syaorans in Tsubasa Reservoir Chronicle comes off like this, since they both use nearly identical styles of kickboxing and swordplay. The only difference is in their magic: Syaoran has inherited the Li family's magic, while the clone has stolen half of Fai's magic. The latter is also far more ruthless in combat, which generally gives him an edge.
Near the end of the Rurouni Kenshin manga, Aoshi fought against another user of two swords who used his own moves against him. It worked for a while until Aoshi dropped his swords and just started beating him with only his fists.
Dragon Ball GT also features an example where the Humongous Mecha Luud can only be destroyed by simultaneous attacks from inside and outside.
Used by Piccolo for solo training in the Hyperbolic Time Chamber.
Naruto does this near the end of the Rescue Gaara arc in Shippuuden. Clones of Gai, Lee, Neji and Tenten attack after they remove the seals that hide Sasori, Deidara and the dead Gaara inside the Akatsuki lair.
Shikamaru's basic technique forces his opponent to perfectly mirror whatever he does. He subverts this trope in his first one-on-one fight by easily beating a perfectly symmetrical opponent. He and Kin both throw shuriken at each other. While dodging the shuriken, Shikamaru forces Kin to slam her head against a wall behind her.
Ptilol and Cyprine in Sailor Moon S were also one person split into two. They are finally destroyed when an attack from one mistakenly hits the other.
In an episode of Rockman.EXE (Mega Man NT Warrior), an evil alternate universe version of one character shows up. The inevitable fight eventually ensues. This trope is taken to the point that when the two use their Dice Bombs, they both roll the same.
In a different dopplerganger fight they start out equally matched, but then the doppleganger starts predicting the others moves and starts countering with opposite attacks instead.
In Sonic The Hedgehog The Movie Sonic faces Metal Sonic; a robot programmed to think and fight exactly like him. Naturally, they spend half the fight simply canceling each other out.
Sonic: You may know everything I'm going to do, but that's not going to help you since I know everything YOU'RE going to do! STRANGE, ISN'T IT?!
The final battle between Rushuna and Setsuna at the end of Grenadier, in which they're so evenly matched, their bullets end up intercepting each other more often than not.
The battle between Knives and Vash in the finale of Trigun is similar in this respect.
In Mahou Shoujo Lyrical Nanoha StrikerS, Subaru and her sister Ginga have a mock battle. They have the exact same fighting style and even have two halves of the same device (Revolver Knuckle), so it comes off as a mirror match—after initially looking as though a difference in skill level would dictate otherwise.
Saiyuki both plays this straight and subverts this in both the anime and the manga when an enemy creates clones of the main cast programmed with their entire moveset, with every move he's observed up until the day prior to when he chose to unleash them on the team. The main characters quickly realize they'll just copy and counter all their known moves and switch to trying different things, making quick work of the clones and rendering them a minor nuisance, chiding the enemy that created them by saying "the us you knew yesterday isn't the us that exists today". Hilariously, in the manga, although Goku, Gojyo, and Hakkai figure this out quickly, Sanzo doesn't catch on until they find him and tell him...after enjoying watching him fight against himself for a while.
Shirosaki does this to Ichigo in Bleach during their Battle in the Center of the Mind. Slight subversion in that the hollow is actually capable of using much better techniques with greater finesse, he just wanted to show that he could do everything that Ichigo could just as well.
An example without the appearance part in Black Butler is the duel between Sebastian and Agni in chapter 17.
A novice tries this against Akira in Hikaru no Go. Unfortunately, as noted below, in Go you can't win by mirroring your opponent, and Akira forces him to resign.
In Yu-Gi-Oh!, Yugi and Yami Yugi fight each other using the same decks, the only exception being the Seal of Orichalcos on Yugi's side. Subverted in that after a few turns, Yugi plays Sangan, which shuffles the order of their decks, then Card Destruction to make both draw new hands.
In one of the YuYu Hakusho movies, Kuwabara faces an enemy who can immediately match any Ki Attack he performs, resulting in this trope. Kuwabara defeats the foe by unleashing an enormous burst of energy in order to drain both of them, and then just whaling on the guy, who is physically weaker than him.
Ga-Rei Zero- at one point involves a monster whose entire fighting style is based on this. It copies the appearance and weapons of its opponents, mimics their every move, and can even reflect projectile attacks.
An interesting variation is with the Kyosuke vs Axel fights in Super Robot Wars Original Generation: The Inspector. Initially Axel fights Shadow-Mirror Kyosuke and they grapple with each other and try to overpower one another, and when Kyosuke starts to win Axel surprises him with an energy blast that damages him and forces him to active his hidden Einst power, making him a much bigger target. When Axel fights regular Kyosuke the battle is initially a perfect copy of this, right down to similar animation frames and identical dialogue. However when Axel tries the surprise energy blast, Kyosuke reacts faster than he expects to interrupt it and then open fire on the wide open Axel, as regular Kyosuke turns out to be more skilled fighter than his alternate self since he has no Einst power to rely on.
The first time the Minerva and Archangel battleships engage each other seriously in Gundam Seed Destiny (the first encounter was Archangel refusing to fire on them and instead trying to shake them off) it's kicked off them each firing a single volley from their beam guns and firing a missile salvo, and the cannon shots being absorbed by each ships armor and the missiles being destroyed before impact by each ships point defense guns. Showing that both ships have almost identical functioning (though differing in design) weapons (and that their stock footage for firing them is very similar). After this though the battle quickly becomes more chaotic.
In the miniseries Infinite Crisis, both Superman and Lex Luthor face off against alternate versions of themselves, and the two Supermen (Supermans?) later take on a third version of themselves.
Countdown: Arena is four issues of this trope, as Monarch forces different versions of heroes to fight each other.
However, it's not very faithful- while the Wonder Women may be hard to tell apart, the Supermen's powers are very different (one is an "evolved" Kryptonian who can grab the other two's heat vision beams and throw them around by them, while the other is the super-patriotic Superman from All-Star Batman & Robin The Boy Wonder and the third is Red Son Superman, raised communist) and the others all offer some degree of variation- for example, the Ray fights a Nazi Ray and Apollo, one of the Batmen is a vampire (from Batman: Red Rain) and another is a Green Lantern (from Batman: Darkest Knight), one of the Starmen is a monkey and one is a chick, and... well, the list goes on.
In issue #24 of Archie Sonic, everybody ends up in a fight with their evil twin, but nobody's making headway because they can predict each other's moves. The good guys end up winning easily when the good Sally hits upon the idea of everybody changing partners (which, apparently, the evil Sally doesn't expect). It's not explained why, exactly, the good guys suddenly end up being the better fighters... surely this could have caused them to lose as easily as it could have caused them to win?
The lightsaber duel between Obi-Wan and Anakin at the climax of Revenge of the Sith has a few moments where the student's and master's moves match each other perfectly. Including an instance of them cancelling out each other's Force Push.
Interestingly, this has some basis in the Expanded Universe: Form V of lightsaber combat (Anakin's style) is based on the same principles as Form III (Obi-Wan's), only tailored to be more aggressive. And Obi-Wan mixes some Form V into his fighting style anyway.
In the film version of Ryu Ga Gotoku (Yakuza as it's known in the west) has this in fights between Kazuma and Majima. Epitomized in their duel with shotguns.
Having been trained by the same tulku and possessing the same powers, The Shadow and Shiwan Khan manage to do this with bullets. But only once, because they're both a little freaked out by it.
The fight between Wesley and Cross in Wanted has shades of this, such as when they continuously deflect each other's bullets with their shots.
In Replicant, Jean-Claude Van Damme plays a serial killer and his clone grown by the government to catch him. In the climactic fight, both Garrotte and the Replicant try to hit each other but end up punching each other's fists and kicking each other's legs. The weird thing is, they actually mirror each other's moves literally (i.e. one punches with his right, while the other with his left).
Played for Laughs in Spy Kids 2. Gregerio's and Donogan's blows are so symmetrical that the fight ends up looking lame and painful, such as when they both try to suplex each other.
In Kick-Ass, the protagonist and his enemy wind up knocking each other out at the same time using identical weapons.
"Insanity Prerequisite" in the Whateley Universe: protagonist Carmilla fights demon The Kellith. Since they're just two different aspects of the same person/thing, it gets complicated.
In the novel, The Third Twin - the narrator notes that a brawl between the identical twins could go on for some time as they are almost perfectly matched. Ultimately subverted because it turns out they're not twins, they're clones... and there's more than one.
In Terry Brooks' Elfstones of Shannara, the Witch Sisters Morag and Mallenroh, last of their coven, are identical twins—and as such absolutely immune to each others' powers. This would seem to be a perfect excuse for the two to duke it out relatively harmlessly (which they are only too prone to do, since each blames the other for the death of the man they both loved and whom Wisp claims was literally ripped apart). Except for the fact that when their powers combine, the effects become terribly real. Both only get one shocked moment of realization to wail their agony and hatred of each other before the fire consumed them in their somewhat tragic, Karmic Death.
Tahiri's internal conflict with her implanted Riina personality ends up like this once it comes to blows (in Reunion) - the two forms are literally identical, except for their handedness. Given the particular rules of this fight, it'd be equal even if one of them somehow outfought the other, as Riina demonstrates by charring herself with her lightsaber, inflicting an identical wound on Tahiri. The two personalities end up merging.
Live Action TV
Charmed features a fight like this in the Mirror Universe, between the good and evil version of Phoebe and Paige. The two Paiges keep at this for some time, their specific magic causing explosions that threaten everyone around.
Arrested Development parodies this between the twins George and Oscar Bluth. each man tries the exact same sequence of movements, just to be blocked in the same way everytime.
Happens in Farscape when Crichton is duplicated. Each one is insistent that he is the real one and the other is fake, and in order to prove it he furiously plays rock-paper-scissors against himself, seemingly for hours at a time, and it's always a tie. Some viewers have pointed out that Crichton's pulse pistol is lying on a table between the two, leading to speculation as to what the stakes may have been. Later, even when Crichton plays against a recording of his other self, it's still a tie.
In a Sindbad series, the heroes once fight some masked opponents which mirror all their moves - and as turns out, look like them. this is a scam by an evil wizard
In the Star Trek: Deep Space Nine episode "The Adversary", Odo and another shape-shifter fight. At one point they are fighting with exactly the same moves.
Or instead of dropping Z-Targeting, you could use the Megaton Hammer, which is a lot more satisfying. Making Link face the camera, then attacking with a Giant's Knife or Biggoron's Sword when he pops up behind Link and simply casting Din's Fire are also very effective.
Zelda II: The Adventure of Link also has its Dark Link pull off the same moves as you do. It's not pretty. You can cheat and head to the corner and down stab.
An unusual sort of symmetry, though not from clones, occurs in Guilty Gear XX. Before a story-related fight, Ky Kiske and Sol Badguy both perform a massive set of attacks, with each one being the move that serves about the same purpose with each character, starting with projectiles, going next to aerial attacks, then a chain combo attack, then finally, they both throw super attacks. Everything neutralizes the other attack, and they just end up about ten feet further away from each other for it.
IIRC, there's another version of this, possibly in GGX2#R only, where Sol and Ky clash stand slashes, chain into their "dragon punch" moves and then only Sol does his jumping EX Tyrant rave, which takes off about 25% of Ky's health before the fight even begins.
Although they don't look alike, part of the final battle between Solid Snake and Liquid Ocelot in Metal Gear Solid 4 goes like this.
One moment stands out in particular. After spending several minutes beating each other to a pulp, Snake and his "brother", Liquid Ocelot, each find themselves facing each other and holding a syringe full of fast-healing nanotech. Instead of jumping back to inject themselves or trying to knock away the other's syringe, they inject each other, knowing that the the other will do the exact same thing. Fearful symmetry, indeed...
That was a homage to the fight scene in The Twin Snakes between Liquid and Snake, who were twins... snakes.
Something similar can happen in Street Fighter Alpha 3. Adon (trained under Sagat) has a special intro with Sagat, where they both do identical kicks that end up parrying each other.
Alpha 3 also has Fearful Symmetry intros for Evil Ryu versus Akuma (both trigger the Raging Demon special move, and the screen whites out as they exchange blows before being forced apart) and Akuma versus Gen (Akuma triggers the Raging Demon, Gen blocks each hit, Gen rushes past and triggers his own multi-hit move, Akuma blocks each hit).
The cutscene fights between Luke and Asch in Tales of the Abyss; note that they were both trained in swordfighting by the same person. Helped by the fact that Luke is left handed where Asch favors his right.
The player can actually invoke this and score a bonus scene during the first Duel Boss encounter between them, provided Luke and Asch use Rending Thrust at the same time.
The battles between Dante and his older twin brother Vergil in Devil May Cry 3; both utilize their agility, stamina, big-ass swords, and Devil Trigger abilities.
In the original, this is played even straighter with Dante and Nelo Angelo (who is Vergil, albeit Brainwashed and Crazy). Nelo Angelo plays the role of Mirror Boss, using the exact same sword swings and martial arts combinations as Dante (except for the fact that he has a much longer reach). In fact, part of the key to defeating Nelo is parrying his attacks with precise swings from your blade and then countering while he's caught off-guard and trying to ready another go.
In 4, the battles against Dante himself involve Nero having to fire at him (the boss deflecting your bullets with his own shots) while approaching and then quickly attacking while he's open (preferably via Devil Bringer). This even causes a shift to a quick time event where the two square off with their swords before Nero tries to overpower his foe.
A variant occurs at the end of Terra's story in Kingdom Hearts: Birth by Sleep. After Master Xehanort possesses Terra, and the Lingering Sentiment forms, the two fight. Terranort has the same appearance as Terra ( golden eyes, darker skin, and white hair notwithstanding), but most of Terranort's moves are ones Terra can acquire.
Death Gate has one of these as a puzzle. You face a mirror image of yourself, and since he copies everything you do, you can't move forward since the double is in the way. You get rid of him by casting a suicide spell backwards, which does nothing to you, but the re-reversed spell cast by the double kills him.
In Mega Man 1, the title character has to fight a robot clone of himself. While his movement is his own, the robot will fire a shot every time Mega Man does.
In Dynasty Warriors: Gundam 2, Elpeo Puru and Puru II's story modes, being already intertwined, culminate in a cutscene wherein the two battle in their identical Quebeley Mobile suits, each mirroring the other's moves perfectly. They comment on how good and natural it feels.
Likewise, in "Divided We Fall" the original 7 leaguers all fight the Brainiac/Luthor hybrid's copies of the Justice Lords.
Let's not forget "A Better World" in which the entire Justice League fights alternate versions of themselves. The Batman vs Batman conflict plays this trope to the letter with the mirror Batman insisting he knows everything Batman will do (and for the most part being right)
In Teen Titans Starfire, Cyborg, and Beastboy are pitted against their own inner evils resulting in this trope. The fights end up at best evenly matched and at worst losing to their evil counterparts until they switch adversaries. Evil Cyborg defeated by the physicaly stronger Starfire, Evil Beastboy defeated when animal fangs and claws can't penetrate Cyborg's metal body, and Evil Starfire's questionable accuracy unable to hit Beastboy's agile animal forms.
In the Futurama episode "The Farnsworth Parabox", the two Leelas do this, to no effect. After they lunge at each other and end up simply colliding in midair, one of the Professor Farnsworths tells them "Now, now, perfectly symmetrical violence never solved anything."
Leela: "We're exactly the same! I know all her moves; therefore I have the upper hand!"
Also from Futurama is Flexo, a bending robot exactly like Bender. Whenever they get into a fight, they throw punches and just end up hitting each other's fists.
The final battle between Zuko and Azula in Avatar: The Last Airbender definitely has these moments, often with red and blue flames mirroring perfectly.
Happened earlier during their fight on an airship at the Western Air Temple. They both swing to punch each other (shown in slow motion) and the blast of their flames bursting on contact knock them off the airship.
In Xiaolin Showdown, Clay ends up fighting a mime who can perfectly mimic his movements. Clay responds by punching himself; Clay can take the hit, but the mime can't.
Symbionic Titan has a variation of this: back-to-back symmetry. The two aren't clones, but Lance and Cain's martial arts moves are exactly the same, but mirrored, prompting both to ask the other where they learned to fight. Being that Lance learned to fight on another planet, and the Galalunian technology they find in the G3 base, this laid the groundwork for some sort of connection between Earth and Galaluna, though nothing came of it.
Used as a one-off gag in Gravity Falls episode "Double Dipper", but afterwards there's another scene where multiple clones fight each other normally.
Happens in competitive card games like Magic: The Gathering and Versus a lot, especially at the start of sanctioned tournaments where many players may be using identical decks that did well in previous tournaments due to the existence of websites dedicated to the best builds. Many tournament players have several silver bullets against their own deck in their optional side-deck to use in mirror matches.
There are also a few pairs of cards that seem perfectly matched to one another - for instance, Time Spiral reprinted the 13/13 Krosan Cloudscraper, and the next set (Planar Chaos) has Shivan Meteor, which deals exactly 13 damage.
Also appears in the art of several cards, usually ones that represent shapeshifters. Morphling, Clone, Vesuvan Doppelganger, Spitting Image, and the like.
Mirrored Pairs are a set of cards that are of opposing colors and usually do opposing things. Sometimes, this runs in such a way that both cards cancel each other out, like Red Elemental Blast and Blue Elemental Blast (both counter or destroy a card of an opposing color, and since red and blue are opposing colors, they can very well cancel each other out when used).
When playing black in a game of chess, one possibility is to simply mirror white's moves. This is sometimes called a Russian game.
However, this is extremely easy for white to foil, as all that needs to be done is give a queen or rook a clear path to the opponent's side of the board. If black mirrors, all white has to do is kill the other queen/rook; that piece then can't mirror it, since it's no longer on the board.
The Russian Game (1. e4 e5 2. Nf3 Nf6) is both an example and a subversion. Black mirrors when you wouldn't expect him to (2... Nc6 is usual) but he gets into trouble if he continues mirroring (3. Nxe5 Nxe4?) There are, however, other openings where mirroring can continue for the first ten moves or beyond.
This won't work in Go. Sure you can try mirroring your opponent. But it never works in a center game where it is always the first person that plays that ends up winning because they can complete their circuit before you complete yours.