A Dance Battler is someone who looks like they're dancing when they get into a fight. This takes quite a bit of effort to make it look plausible, but it's not unheard of. Being a good dancer requires a degree of agility, flexibility, and coordination, three things that can go a long way in a fight as well. Plus, it looks cool.
There are several ways to go about this:
Seigfried in Kenichi: The Mightiest Disciple essentially uses a more defensively orientated version of this. He encourages his opponents to get in close and attack him, then secretly uses dancing-like skills to dodge their blow and fling himself around to fake being hit. This lets him wear down and psyche out his opponents, who come to believe he's incapable of feeling pain.
Mugen from Samurai Champloo is untrained in any sort of fighting style, but possess enough raw power and ax-craziness to do whatever feels right to him and still come out on top. His geta sandals have metal plates on the soles◊, so he can block swords with them. The producers call it the "champuru kendo" fighting style. Frequently assumed to have been influenced by break-dancing or capoeira or both.
L of Death Note, inspired by the more talented Naomi Misora. Both are Capoeira practitioners.
The manga Double Arts features the main leads Kiri and Elraine developing a dance-based fighting style, from which the name of the series is taken.
A couple characters in One Piece fight this way, a prominent example being Sanji, who fights entirely with his legs and whose style is based partly on Savate (martial arts developed by French sailors). And then there's Mr. 2 Bon Kurei, who practices Okama Kenpo (basically, weaponized ballet), and Boa Hancock, the Empress of the Amazon Lily island.
Fakir, Kraehe and Mytho in Princess Tutu, all ballet dancers, fight much in the same manner as they dance.
The anime hints that Nemu Kurotsuchi's fighting style might be similar to Capoeira.
Rose's bankai, Kinshara Butoudan works on this principle and on other two, Marionette Master and Master of Illusion. When unleashed, said bankai releases several ghostly dance battlers that surround the enemy and attack it in organized formations, which Rose (who controls the puppets like a conductor controls his orchestra) calls "dances" and "stanzas".
Mahoujin Guru Guru's Old Kita Kita Man could be this... well... he at least dances when battles take place, anyway. Though he later learns all that dancing has made him strong enough to fight monsters.
Rin Ogata from the Ride Back series, who uses her ballet training to make the Fuego mech dodge and evade swarms of combat automatons.
Bob Makihara in Tenjho Tenge both practices Capoeira and is able to use the mystical power of rhythm to predict attacks. The series quasi-Big Bad tries to justify the trope, pointing out that much of modern military terminology grew out of dancing, that almost every culture with martial arts had them grow out of an earlier dancing tradition, and that dancers typically make excellent martial artists.
In Samurai Deeper Kyo, Shinrei possess his own fighting style, his "dancing sword technique".
Similarly, when it's Anko's turn to fight in the Bokurano manga, she uses her dancing experience to make Zearth move gracefully and swiftly so she can catch up with the enemy.
Pokémon has had Ash develop the "Counter Shield" technique, which basically amounts to any Pokemon called to do it breakdancing while using a special attack, which creates a spinning vortex of the said attack, which keeps an opponent's attack from making contact.
Also Ash's Totodile uses this style to dodge attacks.
Let's not forget Rudy from the Orange Islands who makes his Pokémon dance as an exercise. He even has a Starmi who is "proficient in modern dancing" to help it dodge attacks and even has enough spinning power to generate an Electric attack despite being a Water type.
There was also an episode about a girl whose Bellossom fought and dodged this way.
Subverted in one episode when Ash's Bulbasaur whoops a girl's Hitmontop because she concentrated too much on dancing and not on actually fighting.
In Naruto, the anime and games portray Killer Bee's fighting style laced to the core with hip-hop arm gestures that causes it to resemble capoiera crossed with muay Thai, while armed with 8 swords and Tailed Beast power. This goes hand-in-hand with him being in a perpetual "rap" state of mind. The fact that he raps while fighting causes his opponents to think he's completely bonkers. They may be right.
Makie from Blade of the Immortal is the deadliest and most graceful fighter, fast enough to end each slaughter without a single drop of blood on her clothes.
Fabiola from Black Lagoon does Capoeira moves to dodge bullets while dual-wielding shotguns.
The Para Para Brothers from Dragonball GT combine this with Magic Music. Their dancing and music can hypnotize their opponents into dancing as well, leaving them unable to defend themselves from attack.
Madlax is a Gun Fu Dance Battler - who frequently battles with her eyes shut.
Fairy Tail's member Vijeeter Ecor. His magic is applied through dancing and empowers allies and hinders enemies in a surrounding 10 m radius.
Mami from Puella Magi Madoka Magica, when she fights Charlotte, she shoots, swirls and bashes with her rifles. And her strings swirls about prettily too. It doesn't end well for her.
Capoeira is among the many fighting styles Batman has mastered.
An Archie comic had him and Reggie driven to laughing fits over Veronica's "sissy" male ballet dancer friend - until he singlehandedly subdues a gang of tough guys with his moves.
It was in Dennis The Menace (US) too. Dennis went to ballet school and learned a lot of keen new fightin' tricks he never knew before.
When the Runaways have an adventure in 1910's New York, one of the heroes they meet is Lillie "The Spieler" McGurty, who can fly to the rhythm of music. One of her first scenes has her fighting a gang of strikebreakers and she literally dances on their heads.
Xiong Mao, from the French comic Freaks' Squeele, uses a martial arts style called Flamendo. It is described as "a martial arts style with all the trappings of dance".
Subverted in an issue of Jon Sable, Freelance. John and a male ballet dancer friend are confronted by a gang and Jon is bracing himself for a fight when his friend spots the boombox one of them is carrying and puts on a show combining ballet and breakdancing moves. The gang is so impressed they let them pass.
And he fights a capoeirista (minus the afro) played by Lateef Crowder in this clip from his other film Tom Yum Goong, known as The Protector or The Warrior King in English.
The 1993 movie Only the Strong was perhaps the introduction of many action fans to the art of Capoeira and starred Marc Dacascos as a Green Beret who has to clean up his hometown using the aforementioned art, eventually fighting a Big Bad who uses the same style.
At the climax of the movie Zoolander, Hansel (He's so hot right now!) and an enemy goon partake in "Breakdance Fighting", which for the most part just involved doing little dance moves while punching or kicking people in between.
Michael Jackson dance fights his way through several gangsters in the "Smooth Criminal" sequence of Moonwalker, and again in the video to "You Rock My World".
Ed the Ted and his gang in Absolute Beginners. Arguably justified in that it's a musical.
Never Back Down is a fight movie. In one scene, we have a dreadlocked Dance Battle guy and his uninteresting looking opponent. After half a minute of showboating, however, he manages to frontflip himself right into a thunderous single punch, which lays him right out.
The 'Ninjitsu" practiced by the Teenage Mutant Ninja Turtles in the films borrows from several martial arts (including Capoeira), but also heavily from from modern breakdancing (Which allows them to make full use of their heavy shells).
The Thai film Raging Phoenix features several scenes with both b-boy and traditional Thai dance-based fighting styles.
Mei from House of Flying Daggers. Her actress Zhang Ziyi is not trained in martial arts but is a trained dancer so the filmmakers incorporated dance into all of Mei's action scenes.
A variation occurs in The Mighty Ducks. Tammy Duncan trained in figure skating before being tapped to join the hockey team, and she routinely incorporates figure skating choreography into her hockey play, even using it to score a big goal in a crucial game.
Who Framed Roger Rabbit - Eddie Valiant uses his old vaudeville background subduing the Weasel gang with a vigorous song-and-dance number.
Tap-dancing Killer #2 pulls this off nicely in Bunraku, at one point fighting with his back towards the enemy. His movements were based on Fred Astaire.
In Mary Renault's 1972 novel The Persian Boy, the title character, Bagoas, kills an assailant with a particular move we've seen before - in his dance rehearsals. (As a eunuch, he had been given no combat training, and his belt-dagger was supposed to be ornamental.)
Steven Barnes's Aubrey Knight books Streetlethal, Gorgon Child, and Firedance feature martial artists whose practice improves by learning dance, martial arts disguised as dance and a dance tradition which includes martial arts unbeknown to its practitioners.
Most of the viewpoint characters in Steve Perry's Matador science fiction series practice a dance/martial art known as sumito.
The 'Stick and Bucket' dance from the Discworld series, as performed by the Lancre morris men — we never get to see what it does, but any dance that has a step called 'KILL!' and can be reliably used to fend off The Fair Folk must have something going for it (not to mention the Noodle Incident attached)...
Thank Offler the Fair Folk become quite entranced with music. Still, even getting close to one is just begging to lose face, literally.
It was mentioned in passing Moist von Lipwig's main squeeze, Adora Belle Dearheart, was trained as a ballerina when she was younger and can therefore kick like a mule, presumably quite high. Combined with stiletto heels pointy enough to pierce skin without much effort...
P.C. Hodgell's Chronicles of the Kencyrath books feature a matched set of dance and combat moves that are very closely related, to the point that one training game is to switch back and forth between dancing and sparring.
In William Gibson's short story "Johnny Mnemonic," the Lo Teks have a fighting floor that is wired to shift and produce musical beats based on your footing, with the intention of turning brawls into a sort of dance. Molly Millions fights a Yakuza assassin on the floor, and its strange characteristics give her an advantage.
In Steven Erikson's Malazan Book of the Fallen series, there exists a cult that worships the gods of shadow. As part of their worship, they learn something known as "The Shadow Dance". Lostara Yil, a former member of the Cult of Shadow, thinks that the Shadow Dance is merely just some ritual until she discovers that it's very effective at killing dozens of people without much problem.
Apsalar was here. So were lots of other people, until she arrived.
In the Liaden Universe, the menfri'at, taught in some places as strictly dance, is both a dance and a self-defense discipline for pilots.
The Wheel of Time: Whenever someone witnesses a Blademaster in action his or her movements will be described as dance-like; if the opponent is also a Blademaster, the battle will be described as looking more like a dance than a fight.
Thomas Raith in The Dresden Files pulls this off in Changes in the final battle, breakdancing to Molly's One Woman Rave spell with a Falcata in one hand and a Desert Eagle in the other, taking out Red Court vampires by the dozen. It is exactly as awesome as it sounds.
In Seanan McGuire's Discount Armageddon, main character Verity Price is a ballroom dancer/martial artist, and she lets the dancing bleed into the martial arts because of how much the two have in common.
Scarlet of The Ultra Violets, with thanks to her dancing superpowers. She gets marginally more dangerous once her super-strength kicks in.
In Creator/Mercedes Lackey's Literature/Reserved for the Cat the heroine, a trained ballerina, is being given some lessons in basic self-defense. Her strength and flexibility make her better than her teachers think she'd be, and in addition she is able to all on her own develop a self-defense application to at least one of her dance moves.
Talise Lightwind Murphy of The Children Of Man uses a unique combat style based on the use of offensive yellow magic (yellow is the magic of art and performance, and normally focuses on illusions).
One of the minor Smedries in Alcatraz Series has the Talent of being a really bad dancer, which causes him to turn into this whenever he hears music.
From Power Rangers RPM: Eka Darville, who plays Scott Truman (Ranger Operator Series Red), is a pretty good break dancer and incorporated a lot of Capoeira-like moves in his fights. It's averted in the case of Olivia Tennet, also an accomplished jazz, tap, and hip hop dancer, as her character (Dr. K) does not perform many physical stunts (except in "Doctor K" and "If Venjix Won").
In the Super Sentai series Battle Fever J, it's taken to the extreme; all the members use different dance styles in their attacks - Battle France uses tapdancing, Battle Cossack does Cossack jig dancing, Battle Kenya does a strange breakdancing-tribal dance fusion, Battle Japan uses Chinese kung fu katas, and Miss America uses disco moves to fight. However, this is partially justified in that the agent who employed them regularly trains them in Martial Arts.
Faith, when she beats up a whole discotheque in one memorable Angel episode that has unfortunately been yanked off of Youtube.
And Buffy in the Musical Episode "Once More With Feeling". Also worth noting is Dawn's attempt to escape from the Puppet Minions, which is presented in the form of a ballet dance.
Purdey, heroine of the short lived The New Avengers series in the seventies and played by Joanna Lumley, was a former ballerina who practiced a very balletic fighting form, complete with pirouettes and high kicks.
Kamen Rider Fourze's JK is shown to be a good break dancer in the opening, and finally busts out his moves when attempting to dodge an attack from Pegasus Zodiarts and defeating three Zodiarts when he's forced to use the Power Dizer.
In the 1966 Batman series, Batgirl was played by Yvonne Craig, a trained ballerina. In contrast to Batman and Robin's usual rough-and-tumble fighting, Batgirl's fighting style was elegant, full of high kicks and spins, and even ballet-style lifts by Robin or Batman to set up attacks.
On Community, Jeff locks horns with an overbearing tough guy and they schedule a fight; Britta sees it all as classic repressed-gay behavior. When the tough guy's gang breaks into music-video style fighting choreography, she's even more convinced.
Stargate SG-1 has the Jaffa martial art Mastaba (seen most prominently in "The Warrior"), which is actually capoeira with the serial numbers filed off. The producers actually hired some professional capoeira instructors for the episode.
The 1974 hit Kung-Fu Fighting lyrics are all about how a Kung Fu master uses his moves to be a hit on the dance floor with the ladies.
Stacy Keibler was trained in jazz, tap and ballet dancing from a very young age, and on those occasions when she competed as a wrestler she tended to use a lot of cartwheels and pirouetting spin kicks.
Booker T uses breakdance moves as part of his arsenal, including his infamous spinaroonie (which started out as a variation on a kip-up).
SHIMMER's Rayna Von Tosh has the gimmick of a burlesque dancer and so frequently dances before doing moves such as shoulder tackles and elbow drops.
The Dervish Dancer Prestige Class has a vaguely Arabian Nights-flavor to it, including dual wielding scimitars (and much more easily than a non-Dervish Dancer would, too; pictured above).
The Battledancer Base Class from Dragon Compendium is, judging from the fluff, directly based off Capoeria. Gameplay-wise it handles like a Monk with some of the special abilities replaced by Bardic Music.
This is actually an update from the equally obscure class from AD&D (notable for the eventual progression to nine attacks out of every two rounds, or double that if hasted, in an age where most others topped out at two attacks per round). The less adventurer-friendly abilities, mostly the ones that required a group of other dancers to perform, were justifiably removed in the transition.
The second edition SourcebookThe Complete Book of Elves introduced Bladesingers, elvish sword dancers who do quite well in combat.
The classes from the Tome of Battle can learn from a school allowing them to use a number of special abilities based on their concentration checks. How does this relate to Battledancing? Well, there's a 1st level spell called Undersong that changes concentration checks into perform checks. Used together, they allow characters to perform saves or deal damage based on your perform check. In short, you can be dodging attacks with dance and singing people to death.
The feat Snowflake Wardance from "Frostburn" and the item Slippers of Battle Dancing from "Magic Item Compendium" can both make Bards more effective if they dance in combat.
Eilistraee is the Drow goddess of swordplay and dance (among other things). Some rituals of worship and divine magic of her priesthood call to both of these aspects. (Some of her other rituals also involve Nude Nature Dance.)
Wood Elf Wardancers in Warhammer. They have a variety of different dances that give them a variety of combat bonuses, eschew armour in favour of magic protective tattoos, and at one point had a special ability that let them move over hostile units by dancing on the points of the enemies' weapons.
Harlequins in Warhammer 40,000'' also follow this. Their style of combat describes how they move about the battlefield with dancing gestures, tearing opponents to shreds in the process. The Howling Banshees and Dark Eldar Wytches also have some of this.
At the other end of that spectrum, we have the Slaanesh demon Masque, who is almost eternally performing a dance, and claims its victims by literally making them dance themselves to death by exhaustion. Solitaire, legendary figure of the aforementioned Harlequins, is the only mortal who has ever out-danced Masque.
Slaaneshi Daemonettes also fight this way, dancing elegantly while decapitating and disembowelling.
Exalted, of course, has a Supernatural Martial Arts in this fashion. Dreaming Pearl Courtesan Style animates props like wide sleeves, fans, sashes, ribbons, etc and uses them to grapple or attack several times in a round. At the top of it, you can turn into a dream-like floating golden serpent... somehow.
Malfeas the Demon City teach his exalts how to be awesome in both dancing and fighting. Crafty players will quickly put two-and-two together and create Comboes that combine the benefits of his charms. Incredibly destructive Bollywood dance scene ensues.
Momoko in The King of Fighters XI uses Capoeira... or so she says, but it's hard to tell given that she's so tiny. Robert Garcia is also constantly dancing in his regular stance, although he doesn't use capoeira like the others. He just really likes dancing in place like that.
Interestingly enough, the character Blanka from the Street Fighter 2+ lineup is noted in the manual as utilizing Capoeira, the typical "dance fighting style", although this is only evident in his flips, as he fights more like a beast.
In Pokémon Colosseum, Miror B. and his team of Ludicolo dance to a salsa beat while they wait for you to select your next move.
Hitmontop's attacks are all based off Capoiera, as well as Hitmontop's Japanese name, Kapoerer.
Maractus from Pokémon Black and White is apparently this, judging by its name and Pokédex entry. Lilligant also has shades of this, only learning moves with the word "Dance" in them aside from the moves it starts with. Meloetta's Pirouette Forme appears to be a dance battler, judging by its type, Normal/Fighting.
There are a few dance-themed moves than can make many Pokemon into this by default, such as Petal Dance, Teeter Dance, and Quiver Dance. There's also Fiery Dance (which only Volcarona can learn) and Lunar Dance (only learnable by Cresselia, and its Signature Move).
Rikku's Berserker Dress Sphere in Final Fantasy X-2 does Capoeira movements in her idle animation. There's also the Songstress Dress Sphere which has several dances as offensive attacks though they usually just cause status changes.
If Kefka's line of "Dance, Dance!" and his actions when casting "Zap-Trap Thundaga" in the Dissidia subseries of Final Fantasy is anything to go by, apparently he utilizes this trope, presumably under Type D (ie, because he's completely insane).
In Final Fantasy XIII and its sequel, the Demon enemy subtype fights by dancing around the battlefield. It's even stated in some of the game's lore that dancers mimic the demon's movements.
Many Fire Emblem games also have a Dancer class, although only the firsttwo series allow them to fight properly without glitches. Even then, Dancers have far inferior stats compared to other classes, as their real purpose is to grant allies another turn. Fire Emblem Awakening brings back the fighting Dancer with Olivia, and thanks to unlimited reclassing, she can actually fight on par with other units, even when reclassed back to a Dancer.
Duck King from Fatal Fury is an example of the "really good dancer" type, while Richard Meyer and Bob Wilson from the same game use Capoeira. In fact, Richard Meyer is the first Fighting Game character to use Capoeira.
Possibly the only shooter example, and a gratuitous one at that: Vanessa Schneider from P.N.03.
Majora's Mask has Odolwa, the Masked Jungle Warrior, as the boss of its first temple. He's a Type D, perhaps with some Type A thrown in for good measure. Due to his erratic movements, which sometimes stem to leaping to a random point in the room and simply dancing without making any strike, (and the fact he summons dungeon-unique beetle-creatures, which Link has to kill, and swarms of flesh-eating locusts, which he can't do anything about), he's often That One Boss for beginners. He's also an example of Nightmare Fuel for some, particularly due to the fact that he's constantly chanting almost incoherent words throughout the fight. Apparently, translated to English, what he's shouting is "we shall fight!", over and over and over.
And of course, there's Majora itself, specifically, Majora's Incarnation. Definitely type D, including it's moonwalking.
A Type-B example: Dancing is just Shantae's way of saying "abracadabra".
Disco Kid of Punch-Out!! Wii, as his name suggests, disco dances in the ring about as much as he boxes, and dances even more outside of it. He even has his own disco ball above the ring. His Contender-version boxing style incorporates some rhythm, but it's even more noticeable in Title Defense, where he also incorporates exercise, and starts doing jumping jack hooks and the "Disco Flurry" move.
Touka in Utawarerumono. However, it's noted that her swordsmanship is actually needlessly inefficient, though still excellent, and not as good as it really could be if she stopped trying to make it beautiful.
Anji Mito from Guilty Gear uses a sort of 'fan-dance' style using the magical Zessen (Stopping) Fans. Bridget also dances to fight, in tandem with his yo-yo tricks, even dancing in place in his idle sprite. Hence, the two referring to each other as 'performers' when meeting.
While Kingdom Hearts's Demyx doesn't dance so much as play his sitar when you fight him, his servant Nobodies, the Dancers, will force Sora into dancing with them to drain his HP.
Kingdom of Loathing has the Disco Bandit class, where you use disco moves to injure and debilitate your enemies. The class-specific Disco Bandit Nemesis quest lets you learn Rave Combos, which chain together other non-Disco dance moves like a breakdancing spin, the Robot, and the Running Man to cause combat effects.
In the Knights of the Old Republic games, Echani martial arts, espcially the ritual forms, are allegedly very close to a dance style. The Mandalorians mock this, calling them "fey dancers with weapons not fit for Mandalorian children." Still, Echani blades are some of the best ones in-game, and the Handmaiden in the second game isn't to be taken lightly.
In the downloadable Joker missions of Batman: Arkham Asylum, the Joker seems to use mostly a combination of Capoeira, Drunken Boxing, and lethal novelty toys.
In Batman: Arkham City, Catwoman can be this, since her move set is a lot more fluid and ballet-like than Batman's, who uses more brute strength than acrobatics or gymnastics. And Nightwing is another example, having once been an acrobat himself.
And in Batman: Arkham Origins, the Flashback!Joker you play as can be this, since his fighting moves are the same as in Asylum, while his moves are somersaulting and leap frogs. And all this takes place in the Comedy Club, set to the tune of "The Thieving Magpie Overture" by Gioachino Rossini, doubling as a Shout-Out to the hallucinatory fight scene in A Clockwork Orange.
Mileena in Mortal Kombat 9. She dances onto the arena as she makes her entrance, and says "Let's dance!" as her Battle Cry. (She is insane...)
Blades in Baldur's Gate 2, and by extension Haer'Dalis, are supposed to fight using theatrical/dance-like fight moves. Not that you can tell with the graphics.
Jean from Lunar: Eternal Blue is a literal example. She is a dancing gipsy who has a bloody past as an assassin.
It takes a little practice but in City of Heroes attacking repeatedly and quickly means a prolonged battle can often look more like a dance than a fight.
Lucia from Shadow Hearts is a fortune teller who dances while slashing enemies with a fan. She also dances when she casts magic spells.
El Shaddai: Ascension of the Metatron has Armaros, whose first boss fight only features him dancing in the foreground, while Enoch fights his... backup dancers. When you take control of him, his actual fighting style is pretty dance like as well, and you can actually make him dance outside of combat if you feel like it. One of Enoch's weapons, Gale, is commanded through dance-like movements while on the ground as well. It is possible to wield the Gale in the aforementioned boss fight.
Michael Jackson's Moonwalker has Michael Jackson going around various stages... rescuing little kids from suit-clad gangsters. His moves? High dance-kick, spin-and-throw-hat, and the special "make everyone imitate your dance and then fall over and die when they can't keep up with your straight, 45-degree angle pose".
Hazama of BlazBlue has a fighting style that resembles dance. This, combined with his outfit and villainous role has lead to fans nicknaming him The Smooth Criminal.
The official profile of Yurika Kirishima of Project Justice lists one of her hobbies as ballet, and it shows in her fighting style. A number of her moves show influence from the dance style, most notably her dashing hard kick in which she performs a grand jeté.
Kokoro no Hata from Touhou uses a fighting style that incorporates props and moves from Noh theatical dances. This is unsurprising since she is a Youkai borne from from the legendary 66 Kagura/Noh masks used by Hata_no_Kawakatsu, the founder of Kagura (which is the predecessor of Noh).
Juliet Starling from Lollipop Chainsaw is a cheerleader who dances while swinging her chainsaw around.
Stanley says that rocking out is better than dance fighting. "It's Titanic. It's the highest music there is."
Headbanging appears to be one of the most basic forms of dance fighting and is probably one of the weakest. In addition, Wanda is ordered to do a 'Safety Dance,' which appears to increase a units defense.
In Metro City Chronicles, Hybrid eventually ends up converting her dance skills as a ballerina into a fighting technique.
One Smosh Shut Up! Cartoons series, Oichi High School Battle, has an episode where Oishi rejects Reif's offer for a date, and because of this, Reif tries to get Oishi to see Puss In Boots Part 2, but Oishi says that Reif is going to have to battle her boyfriend, Mucusance, in "combat." A dance battle ensures between Reif and Mucusance. Mucusance wins due to him being good at dancing and eats Reif.
Atop the Fourth Wall features the Ninja Style Dancer, who will beatdown his opponent while dancing to music.
Some female Freelancers, such as Carolina and Connecticut, rock this trope, whereas Tex has too aggressive a style and South relies much more on guns. The Fem!Surrectionist, as the Knife Nut female ODST is known, also has some aspects of this.
Played straight half a season later when Aang and Zuko learn a fighting form that doubles as (and is called) a dance, which Zuko is less than enthusiastic about. We later see him using a kick a lot like the one Mugen is doing in the above pic. Except with a lot of fire.
It should be noted that Zuko actually used Dance Battling quite often early on in the series. This had the downside of wearing him out within moments as seen in his fight with Zhao, and he eventually stuck to using the more basic forms.
Korra has used Dance Battling in the few times we've seen her fight so far - she's extremely graceful and uses lots of leaps and spins, in addition to great sweeping gestures with her arms. This, and all of the Dance Battling from the previous show, is Justified by the nature of bending - the movement of the elements flows with the movement of the bender's body, which naturally sometimes calls for something more complicated and expansive than plain old kicks and punches.
Desna and Eska, Korra's cousins, also use a lot of acrobatics in their waterbending.
In The Three Caballeros, at the climax of Donald Duck and Joe's visit to Bahia, two men get into what is probably supposed to be a Capoeira fight (which would make sense since the martial art has origins in Brazil). Their shadows even temporarily take the form of two roosters fighting, which is said to be what Capoeira takes it's name from. However, they seem to be doing more dancing than they are fighting.
Parodied in The Simpsons; Moe is teaching a "Dance Fighting" class at the Learning Annex, and demonstrates a move that starts out like he's gonna dance, then he pulls out a gun and fires off two shots.
Just look out for someone doing a Cossack dance in an old cartoon - there will be butt-kicking.
Robin from Teen Titans is this, to varying degreesof realism. The blatantness of it varies, but it's extremely apparent when he's fighting against someone else who excels at martial arts (most notably Red X, who is also a Dance Battler, as he shares Robin's style of fighting) or someone whose fighting style involves being huge and throwing a lot of heavy things at him.
Bugs Bunny was fond of this trope - he gets rid of a malicious hobo on a train car using some balletic moves, and ticks off a bull in the ring with a Mexican dance with face-slap percussion.
Popeye - "The Dance Contest" and "On Our Way to Rio" are just two cartoons where Popeye uses dance to beat up Bluto.
Bob's Burgers - Bob's daughter Tina takes up Capoeira because she has a crush on the teacher.
In Duck Dodgers while trying to distract the "Mother Fudd", The Cadet asks "What would Gene Kelly do at a time like this?" So he starts dancing on his giant head.
In Samurai Jack, the leader of the big party Jack stumbles into in "Jack and the Rave" fights Jack and is easily the samurai's equal in hand-to-hand combat, though unlike other rap-themed fighters, he fights exclusively with his arms and hands, using hip-hop gestures to punch, chop, and defend. (This doesn't seem to be based on any martial arts in particular—his fighting just looks like rapping on fast forward.) The DJ, however, is no match when Jack gets his sword back.
In the latest incarnation of Teenage Mutant Ninja Turtles, Splinter tries to instruct Donatello not to overthink strategy during a fight, and instead live between thoughts. To demonstrate, he launches a training exercise against Michaelangelo, who has just entered the room listening to his music. Mikey nimbly dodges the attacks in time to the music, until Splinter decides the lesson is over and trips him with his tail.
Xever, Shredder's left-hand man, fights with a combination of graceful and powerful Capoeira and dual-wieldedbutterfly knives, making all four of his extremities deadly weapons. After he mutates into Fishface he loses his combat abilities for a little bit, until Baxter Stockman whips up a pair of robot legs for him, making his Capoeira even more dangerous.
Parodied in Gravity Falls — Sev'ral Timez "dancing aggressively" is treated as if it were actually dangerous or a viable method of combat, despite not actually including the "battling" portion of this trope.
Skipper became this temporarily in Penguins Of Madagascar when the magic-practicing chimps stole King Julian's "groove" and transferred it to Skipper.
This is parodied and subverted in American Dad!, Those Two Guys Terry and Greg are angry at Stan and intend to beat him up, they begin doing flowing, streaming and ineffectual moves which Stan mocks, when one of them promptly sucker punches Stan to the ground with a Groin Attack.
Stan: That wasn't campy at all!
Dance and traditional means of livelihood often share similar movements according to the standard academic theories of dance, especially folk dance. Martial arts are part of the same physical traditions and often share striking (so to speak) similarities.
That is not to say that all traditional dancers are can fight. Very often the dance traditions use larger, more flamboyant and expressive movements designed for visual appeal. And it does not mean all martial artists can dance, either. But there is a degree of overlap, especially in traditional cultures. Many of the attributes that make a good dancer - strength, endurance, grace, balance, rhythm, timing, physical presence - are also found in warriors.
To further complicate matters many martial arts have an explicit dance component. "War dances" all over the world incorporate movements and emotional content from their combative tradition. The purpose may be to create group identity, impress the opposite sex, entertain, compete non-violently for status or frighten enemies. In some traditions combatants show their form by shadowboxing, often to music. A vastly inferior opponent can step down without losing face or risking injury at this point. Or participants may show a false weakness to the surprise of the opponent when they fight. Or at least it gives the audience a chance to lay down bets.
A very incomplete list of examples:
Africa and Afro-Caribbean: Many martial arts either originated from dances or were concealed by practicing them as dances, like Maculele, Mandingue, Laghia de la mort, Mayolč and others
Brazil: Capoeira is believed to have its roots in West African dance/fighting traditions. It is practiced to music and singing. The practice of Capoeira was generally illegal at the time of slavery. It was hidden in public by disguising it as dance. Capoeira co-evolved with the Brazilian Samba dance tradition.
Breakdancing: Supposedly invented as a ritualized substitute for actual combat, taking a lot of cues from Capoeira above. Early moves were influenced by Hong Kong action films (hence the name, incidentally, of the Wu-Tang Clan, which came from the same hip-hop culture).
China: In recent days many but by no means all forms of Chinese martial arts have evolved from combat to an athletic/gymnastic competitive display which has many of the attributes and requirements of dance performance. The degree to which this has occurred varies widely from school to school.
Europe: Most of the dance/fighting traditions are extinct, but some examples of martial dancing with and without weapons still exist in Eastern Europe, the Balkans, Scandinavia and Basque country.
Notational systems for dancing and fencing came about around the same time in Western Europe, and had several similarities.
India: Too large a place to generalize about, but examples abound. The ancient martial art of Kalaripayitt is very closely related to classical Indian dance and to a number of Yoga traditions.
Indonesia, Malaysia and the Phillippines: The dance and martial cultures are nearly inseparable. Whether a particular movement is aesthetic, competitive Olahraga or deadly Silat is more a matter of intention than anything else. Traditionally dance and Silat are performed to the Gamelan orchestra. In the Central and Northern Philippines the connection is more tenuous.
Japan: Swordsmen Yagyū Munenori and his son, Yagyū Jūbei Mitsuyoshi, often used terminology of Noh drama's dancing when discussing the timing in swordfighting. The modern Japanese martial art of Aikido is often considered dance-like because of its grace and fluidity.
Korea: While there is great academic and hoplological disagreement about Taekkyun as a martial art rather than a game it shares similarities with Korean martial arts and dance
Polynesia, New Zealand: Men's dance (Hula, Haka and other names) and martial arts are very closely connected sharing many motions and training methods. New Zealand's All Blacks rugby team does a traditional Maori haka war dance before games. It is unmistakably martial. On several occasions a haka performed by opposing Polynesian teams has led to pre-game fights.
Interestingly enough, Bruce Lee was also an award winner in cha-cha. It's this expertise in dancing that gave him his expertise in martial arts footwork. Or possibly the other way round.
As the saying goes: "A warrior who cannot dance is awkward both in peace and at war."
Bruce Lee developed Jeet Kune Do to incorporate any movements that were effective and felt natural. While it has a philosophy, there is no such thing as the Jeet Kune Do "style." If you felt comfortable doing the cha-cha in a fight, more power to you.
John Travolta once said that being a skilled dancer helps him do the choreographed fight scenes in his action roles. Of course, how he'd do in a real fight is anyone's guess.
Likewise, Jackie Chan is trained in Chinese Opera, and uses its movement techniques in his fight scenes. How he'd do in a real fight is not up for debate.
Sugar Ray Robinson was a dancer in his youth before becoming a boxer. You can see the influence in his fights, especially when he simply moves around the ring. It's as though he glides across the ring.
Okinawa: When Karate was outlawed for a time by the ruling Japanese, the Okinawans turned their kata (forms) into dances in order to keep training without arousing suspicion.