"Hey, can someone explain to me why I'm always fighting skanky chicks who fly? I mean, Sabine, Samantha, Tsukiko... I bet even the druid's hawk was some sort of a bird-hussy. I should take a level of ranger so I can choose Favored Enemy (Airborne Tramp)."
An unspoken version of Wouldn't Hit a Girl, when there's a team with one Action Girl, and there's one female opponent among several men, the two will always take care of each other. She might take out one of the guys, too, but the men will keep to themselves. It's not universal enough to list aversions, but it's definitely noticeable.
Essentially, when the Hero needs to fight a girl, he must get a Pinch Hitter to take his spot. Sometimes the Hero's girlfriend gets this as her role. Often the job of The Chick in the Five-Man Band is to smack the supervillainess around, essentially becoming the team's Designated Hitter for all female villains.
If one girl is the morality-reversed equivalent of the other, the odds are increased exponentially.
This tends to be the end result of a basically gendered aspect of many superheroes: male superheros tend to have a generally male Rogues Gallery, while superheroines tend to have female villains. Thus, a Legion of Doom team-up tends to be fought along gender lines.
Might lead to a Cat Fight, but more often nowadays the fight is otherwise played seriously. Compare Counterpart Combat Coordination.
Examples:
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Anime and Manga
The Angewomon/LadyDevimon catfight in Digimon Adventure comes to mind. Though in this case, it's more Angewomon wanted to take LadyDevimon out herself and rebuked anyone who tried to help, and LadyDevimon was Piemon's Dragon. The fight was later repeated in Digimon Adventure 02, with this LadyDevimon serving Daemon instead.
In Digimon Frontier, Izumi has the most fights against Ranamon, and Ranamon was her only kill and scan in the entire series.
Averted in Digimon Savers. Kurata assembles a team of Psycho Rangers to fight the main Power Trio, but the female members of each don't battle each other. Instead, Nanami takes on fellow Teen Genius Touma and Yoshino faces her Stalker with a Crush Ivan. In fact, Nanami and Yoshino had almost no interaction at all during the series, unusual in that this was the Digimon iteration in which fanservice started being a thing that regularly happens.
Semi-played in Digimon Xros Wars - Mervamon was one of two Digimon present for the final fight against Lilithmon, but she was working together with Beelzebumon for the entire fight, and he's the one who takes Lilithmon out.
The men are sent off to Shishio's lair, while the rest of the gang stays behind - and are subsequently attacked by the rest of the Ten Swords. Since the show lacks a variety of villainesses, Kaoru and Misao get their first and pretty much only real fight against Kamatari... a crossdresser.
Weirdly, the trope was almost not-followed-by-the-letter back then. Okina's division of enemies at first had Kaoru and Yahiko assigned to face Hen-ya, and Misao would face Kamatari alone. But then some insults from both parties reassembled them to what it ended up as. In fact, the original division would've made far more sense, as letting a novice swordsman such as Yahiko to fight by himself is not a good idea in any way...
In Naruto: out of twenty competitors in the Chuunin exams, six were female. Sakura and Ino, past rivals, fought each other, as did Tenten and Temari. Averted with Hinata (who faced Neji) and Kin (who faced Shikamaru). Though it should be noted that in the absence of a female hero, Shikamaru will always ends up fighting the female villains. Also averted in Part II outside of fillers.
The Naruto movies seem to avert this, especially the early ones. In the first one, Sakura and Sasuke collaborated into blowing up a female-male duo, while in the second movie, Naruto, Sakura, Shikamaru, Kankuro and Gaara faced three female villains (whom they killed.. quite gruesomely). Played straight in the third movie, where Sakura fights the only female villain in the film.
In Shaman King, it is noticeable that one of the two all-girl teams, Hao's Hanagumi (Team Flowers), fights two battles against three females- once against Anna, Tamao, and Jun, and another against the team "Magical Princess".
In Pokémon Special, this doesn't extend to sanctioned matches, such as gym battles, but against bad guys, yup, girls tend to match up with each other. If genders don't match up in those ultimate battles against good and evil, that's just because the gender ratio isn't evened out as many girls will paired up against each other, and whoever is left gets to fight a guy.
Justified in Pokemon Best Wishes with Pidove VS Snivy. Snivy (female) had been stopping all of Ash's attempts to capture it by using Attract on all of his pokemon. Then out comes Pidove, whose gender Ash was unaware of, and she proved immune to Attract due to also being female. It's a Designated Girl Fight since Pidove was the only pokemon able to fight Snivy.
Let's not forget that Yoruichi fought Soi Fon (one of two female captains in a group of 13). Orihime fought a female hollow to protect Tatsuki, while all the other boys fought male hollows, though the thing wasn't especially feminine looking.
Averted later when Toshiro fights Harribel and Soi Fon, Baraggan. Ishida also fought Cirucci.
Played straight in the Substitute Shinigami Arc, with Rukia facing Riruka.
And averted in the Vandereich arc: Bambietta fights Komamura, Soifon fights a male Vandereich and Rangiku tag-teams with Toshirot to fight another male.
In Gun X Sword, the first time we see Fasalina in action Carmen is the only one around to fight her, this is turns into a challenge so that Carmen is always looking for Fasalina, conveniently pairing them in fights.
In Hellsing: Seras Victoria kills Jessica, the female vampire in volume one, then she fights Zorin Blitz in a big battle. Although later it seems she was going to battle the Captain, that fight ended up more about Pip vs Captain with him giving the deadly blow.
Well, Pip did deliver the final blow, but that's it. Unless guiding Seras during her duel with the captain counted as doing something.
Semi-averted in Fullmetal Alchemist. Riza Hawkeye is the only female member of Mustang's team and Lust is Father's only daughter, so naturally an altercation between the two occurs. However, this isn't really a fight so much as Hawkeye redundantly shooting Lust repeatedly until Mustang comes along to finish things.
Bizarrely played with in One Piece. When Ivankov is breaking out of Impel Down he's confronted with one of the wardens, the only female among them. In order to fight her, Iva uses his Devil Fruit powers to physically turn himself into a woman.
Played with in the Baroque Works Saga - amongst the final team that fights the heroes, there are two girls. One of them, Miss Merrychristmas, is not exactly... ladylike. She, along with her partner, fights Chopper and Usopp. Miss Doublefinger, on the other hand, who is a typical Dark Action Girl, have a one-on-one fight with Nami.
Meanwhile, Nami fought Kumadori for a while before she switched places with Chopper.
Zig-zagged in the CP 9 Saga: The CP 9 have one female member, Kalifa. At first she fights Sanji - he is much stronger than her, but the fight still ends with obvious results, due to Sanji rather wanting to die than kicking a girl. A short while later she is pitted against Nami, and we get the straight example.
Averted in the Punk Hazard arc. Monet, the female on Clown's team, fights male Zoro and female Tashigi together, with Zoro doing most of the work. This fight also contrasts him to Sanji - Sanji would have fallen over at once to Monet's sex appeal, while Zoro has no problems chopping her into tiny bits (luckily for her, she has a Devil Fruit preventing this from being fatal).
Also averted in Thriller Bark, where Perona ends up fighting Usopp.
Also zig-zagged at Little Garden, where the crew is attacked by four Baroque Works agents, including Miss Valentine and Miss Goldenweek. Miss Goldenweek only plays a passive role in any fights, though, and Nami and Vivi are quickly incapacitated, leaving Valentine to hand Usopp his ass until they're freed and one-shot her.
In Fairy Tail, most of Lucy's 1vs1-opponents are females (Shelly, the brainwashed Juvia, Angel, Flare), but she has also defeated males (Bixlow and Byro). Erza however fights usually against the strong ones (The Dragon guys), with a few of them being female (Ikaruga, Erza Knightwalker). The Daimatou Enbou plays this tropes straight where almost every female fights another female (Lucy vs Flare, Mirajane vs Jenny, Kagura vs Yukino, Wendy vs Chelia). It takes Up to Eleven during the Naval Battle where six of seven participants are females and fighting in swimsuits. After that, there is Erza vs Kagura vs Minerva.
Comic Books
At least once Superman, who won't hit a woman, has stepped aside and let Wonder Woman take care of things.
Wonder Woman generally tends to have a more feminine Rogues Gallery than most heroes, partially because of this trope.
The Justice League comics have the Crime Syndicate of America, an evil version of the Justice league from a Mirror Universe. In their first (Pre-Crisis) battle in the comics, the authors mostly avoid the common cliche of having the characters fight the mirror versions of themselves. The one exception is Superwoman, the evil counterpart of Wonder Woman, who fights Wonder Woman because they didn't want to show a man and woman fighting.
They used it in Runaways, which was particularly irritating since they're usually pretty aware of superhero tropes. The fact that one of the girls involved had a mind-controlled dinosaur makes it only slightly better. Granted, girls tend to outnumber guys on this team.
Averted in Robert Rodi's Codename: Knockout series. Angela and Go-Go are fighting their British counterparts and losing... so they switch "dance partners".
When the X-Men first fought Alpha Flight, Storm and Snowbird went at it, even though Storm's powers were a better match for Shaman's and Snowbird had more in common with Wolverine.
Also, during a battle between the X-Men and Magneto's first Brotherhood of Mutants, Jean Grey was more than eager to fight against the Scarlet Witch, as the guys wouldn't fight her.
The Marvel vs. DC/DC vs. Marvel miniseries had Storm fighting Wonder Woman (the two most popular heroines in their respective universes) and Electra fighting Catwoman (the two Femme Fatales). It's averted, however, when teen heroes Robin and Jubilee are paired off, though he does manage to defeat her without hitting her.
In the early issues of Maximum Carnage, Black Cat immediately went for Shriek when Team Venom found Team Carnage. Justified in that Shriek was likely the only one of the villains that the non-super-powered Black Cat would have had a chance in defeating.
Archie's Sonic the Hedgehog comics featured a mirror universe in which the Freedom Fighters were evil, and inevitably this led to a confrontation between them in one issue. Initially this fight seems to go this way, as Princess Sally fights her own Evil Counterpart, but the trope is quickly subverted when the heroes realize fighting a mirror image is difficult...so they switch partners. Cue Sonic literally punching the evil Princess Sally in the jaw.
Fan Fic
In the Tamers Forever Series there is a brief battle between Rosemon and Sakuyamon. However this is actually justified as both these women are actually the most competant fighters in the area. (not including those who are borderline catatonic)
In Ultimate Re Imaginings, Emma and Natasha fight, although this is justified as the latter is trying to kill the former and aren't pulling punches.
Film
In the final battle in Hot Fuzz, Skinner's attack secretary is taken out by Doris, the one female police officer. This does not go without lampshading.
Mean Girls has the Matheletes sudden death round, Cady vs. Kraft.
Superman II has the evil Kryptonian woman Ursa getting punched out by Lois Lane (and apparently falling to her death) after getting depowered. Superman himself never hits her, even when she's as strong as he is.
In Van Helsing, the female sidekick kills Dracula's last vampire bride, but does not get to kill Dracula, even though she was supposedly fated to do it.
In Cradle 2 the Grave, Gabrielle Union fights Kelly "Lady Deathstrike" Hu.
Jinx vs. Miranda Frost in Die Another Day, although the James Bond series has featured occasions where Bond has fought and killed women.
In Batman & Robin the movie, Poison Ivy was reserved for Batgirl. She takes out both Robin and Batman with astonishing ease in her lair — should Barbara not have butted in and become Batgirl all by herself, Poison Ivy would actually have won.
Averted in The Dark Knight Rises, those who predicted the spoiler in advance were expecting a Catfight between Talia Al Ghul and Catwoman, but it didn't happen.
In Dragonball Evolution: Goku fights Piccolo alone while Bulma and Yamcha run to safety. Then, Yamcha disappears inexplicably while Bulma fights Piccolo's female minion Mai. This may be because there's no way Bulma could help Goku fight Piccolo, but there's also no way she'd stand a chance against Mai either ... at least, not the way she's been portrayed.
The older Dragon Ball: The Magic Begins averts this by having Pigsy shoot the henchwoman.
Bulletproof Monk has one where Action Girl Jade gets in a fight with The Dragon, who happens to be the Nazi villain's relative. It's Jaime King versus Victoria Smurfit; for a fight to the death, hotness ensues remarkably quickly.
Push. Cassie and the Triad girl fight. Double points since they had the same power as well.
The fight between Evy and Anck-Su-Namun near the end of The Mummy Returns. The first film has a subversion, with Jonathan fighting Anck-Su-Namun. Although Evy and Anck-Su-Namun have significant history that would make them want to fight for personal reasons, and Evy is far more capable than Jonathan. It's less about not wanting to hit a girl and more about not getting your ass kicked by a girl.
Subverted in Conan the Barbarian. It looks like this is going to happen, as Valeria goes after the Princess while the boys are holding off an army of mooks — but Valeria is far too badass to get into a catfight, and promptly passes the (now stunned and tied) princess to Conan.
It has Knives vs. Ramona fighting for Scott's affection. There is also Ramona VS. Roxy.
The Ramona vs. Roxy fight has an interesting half-aversion partway in. It's pointed out that Scott has to be the one to finish off Roxy, but Scott Wouldn't Hit a Girl. To deal with this, Ramona simply gets behind Scott, grabs his arms, and uses him as a People Puppet to continue fighting Roxy.
Melina vs. Lori in the original Total Recall 1990, though Quaid still gets to finish off Lori.
The live action Tekken movie has Nina and Christie face off in an intergender tournament. This is also averted when Nina and Anna try to assassinate Jin and Christy kicks plenty of ass against Kazuya's soldiers.
Dredd. Averted. Anderson is wounded in the final battle by a mook and it is Dredd that deals with Ma Ma.
Mission: Impossible, in which token heroine Jane Carter squares off with token sexy female assassin Sabine Moreau.
Subverted in X-Men: First Class in the final fight as the enemy team has one girl while the heroes have two. None of them interact as Angel gets stopped by Havok and Banshee while Mystique helps Beast take out Azazel.
X-Men: The Last Stand plays it straight, however, and has Storm squaring off against against Callisto on two occasions.
Resident Evil: Retribution features Alice facing off against a brainwashed Jill Valentine and an evil clone of Rain Ocampo from the first movie. There's also a mini-scuffle between her and Canon Immigrant Ada Wong early on.
Because Rand refuses to hurt women. Different from most implementations of this trope in that the implications of his unwillingness to fight women are actually addressed in the books.
Practically deconstructed, when Moiraine has to step up and take on the vastly more powerful Lanfear because he can't make himself fight her, and apparently dies in battle. Rand has a Heroic BSOD as a result.
While Voldemort is fighting two teachers (one of them female) and an Auror, his Dragon Bellatrix Lestrange is fighting three schoolgirls...and she gets offed by one of them's Mama Bear.
According to Word Of God it's also Bellatrix who kills Tonks.
Earlier in the seventh book, Luna Lovegood stuns Alecto Carrow presumably so Harry wouldn't have to.
Also notable is the fifth book when Dumbledore uses his magic to bring the statues in the Ministry of Magic to life. The statue of the witch goes for Bellatrix.
The Faerie Queene, Book 5: The female knight Britomart fights the evil Amazon queen Radigund because her boyfriend Artegall had to learn the hard way that Wouldn't Hit a Girl should not apply when said girl is trying to kill you.
Lampshaded, after a fashion, in an episode of Dukes Of Hazzard: when the group pairs off for the big brawl at the end of the episode, Cooter laments that the only person left for him to fight is a girl. Cue Daisy, who steps forward and says, "Oh, no, she's mine!"
In the BBC series of Robin Hood, whenever the outlaws fought the law, Kate would always make a beeline for Isabella, the Veronica to her Betty, and her rival for Robin's affection. It was only a matter of time before the catfight ensued.
In Power Rangers, whenever both heroes and villains have combatants of both genders on the field, the guys tend to break off into one skirmish while the girls have their own fight. However, averted when at least one side is composed of only a single gender (or even a single person as is normal for villains; with either the Monster of the Week or The Dragon), as the neither side will hold back due to gender.
Done very frustratingly when Power Rangers Ninja Storm and Power Rangers Dino Thunder crossed over, where the mind controlled Ninja Rangers team squared off against the Dino Rangers; as the show broke its unofficial color-coding rules to have the female Blue Ninja Ranger and Yellow Dino Ranger fight each other instead of their like-colored male counterparts.
Similarly, in Firefly, Inara heads off on her own to try to stop Saffron's plans twice. The first time, Inara loses a martial arts catfight to Saffron, who doesn't get away for long. The second time, Inara gets the upper hand by watching the end of the crew's impressive Gambit.
In the Star Trek The Original Series episode "Mirror, Mirror," it's Uhura who steps in to disarm Marlena Moreau when the latter pulls a knife.
In the episode "The Gamesters of Triskelion", Kirk, Chekov, and Uhura face two male and two female gladiators. Kirk and Chekov take one male each, while Uhura has to fight both women.
In a frist season Next Generation episode, Tasha has to fight a chick to the death for the amusement of their hosts. Dead girl gets better.
In Chuck, any and all female spies will be taken care of by—you guessed it—Sarah. The traitor in the C.A.T. Squad? Check. La Ciudad? Check. The female spy at her high school reunion? Check. And that fight was wet.
Used in the Sliders episode "Data World". A villain sends a male and a female Mook after the Sliders. When the male shows up, the three guys fight him while Maggie (the team's Action Girl) simply runs and hides. When the female arrives, then Maggie steps up and declares, "This one is mine!"
Unnatural History: Maggie and the female scientist in "Thor's Slammer".
A fair number of episodes of Alias have this. Sydney's a trained spook, and always has a gun, but if a female enemy spook shows up, the gun will be kicked from her hand, and the two of them will throw down.
Subverted in the season 3 finale of Merlin. Gwen goes for Morgana but, being untrained in sword fighting, is easily defeated leaving it to Merlin to take her on. Also it's Gaius who takes out Morgause.
Wizards Of Waverly Place: Alex vs...Dark Alex, I guess, and Mason vs Dominic. Slightly justified in that Evil Alex was Alex's clone. Weird in that the same actor played them.
Professional Wrestling
Very common in Professional Wrestling during random two guys + one chicks tag match. When the female wrestler from one side tags in, the one on the other team will inevitably do the same in a matters of seconds. Often it's actually in the rules that they must tag in. In fact, this is given its own name. Frequently they'll mention the difference between a "Men fight Men, Women fight Women" match and an "All Bets are Off" match. One is an "Intergender Tag Team Match" the other is a "Mixed Tag Match." The WWE only has men fighting men and women fighting women.
In recent years, there have also been an increased number of regulations enforced either by the networks or the companies themselves that they are not allowed to show Man-On-Woman violence, which pretty much means mixed gender matches are impossible, unless it's completely one sided with women beating on men without the man even getting a shot off, which in turn would be completely anti-competitive and would seem to reinforce the problematic Abuse Is Okay If Its Female On Male.
Super Paper Mario, where Peach and Mimi face off one on one at the end.
The slap fight between Tifa and Scarlet near the end of the second disc of Final Fantasy VII.
Averted in The King of Fighters '97. The New Faces team is more or less an evil counterpart to Japan's Hero Team, but the resident lightning user (Shermie) is female. Although considering that she's Benimaru's counterpart, perhaps it's being played straight...
Also averted in the Treasures of God path. You can make Chizuru fight Shermie, but this is completely optional.
In general, fighting games tend to zig-zag the trope to Hell and back. You can have a Designated Girl Fight if you choose an Action Girl as your chara and have her face a female enemy, but there are more than one ways to avert this unless said fight is pre-determined by plot and/or paths.
Used to a degree, during the two-on-two boss battle with Wesker and Jill. If Chris keeps Wesker's attention on him, Sheva will engage and attempt to restrain Jill to keep her out of the fight.
Averted if you play as Sheva, where Chris will offer to take care of Jill while she deals with Wesker.
In Samurai Warriors 2, Oichi and Nohime's Gaiden battles are literal Designated Girl Fights, as they challenge each other (and all of the female characters, plus RanmaruMori) to see who the fairest in the land is. At the beginning of said battles, an absolutely delighted Oda Nobunaga eggs them on.
In Dynasty Warriors 6, when Yue Ying and Zhen Ji encounter each other at the battle of Han Zhong, they exchange insults about each other's husbands. Depending on which side of the battle you're playing, the dialogue will change slightly, but whichever one is on your side will land the final zinger, and the other will become enraged and go into hyper mode.
Subverted in the opening cinematic: It at first appears that FF6'sTerra and FF8'sUltimecia are having a magic duel, but it's actually a trick: Ultimecia is working with FF2'sEmperor, hanging back on the sidelines, to make Terra fall into one of his traps.
...And now it's evident that, of the three female protagonists who were prominent in the 12th cycle, only Tifa adhered to this trope and ended up facing off against another woman (Ultimecia); Yuna was pitted against the Emperor (for what he did to Tidus and Jecht), and Lightning remained against Garland. And, in another aversion (...sort of?) though the Cloud of Darkness isn't technically female (on account of being an Anthropomorphic Personification), its opponent ended up being Laguna (whose leg crampspromptly started acting up).
Inverted in Summoner, when Jekhar and Rosalind fight Sornehan and Galienne, the player might be tempted pair them up in this fashion, but Sornehan is invulnerable to physical damage, while Galienne is invulnerable to magic, which makes such a match-up Un Winnable since Jekhar is The Big Guy and Rosalind is a White Mage.
In Street Fighter IV Chun-li and Cammy's designated rival fights are against Crimson Viper. Taken further in Super Street Fighter 4 where the fight is against the new bad girl Juri.
And then it's averted when Chun-Li is either The Rival or one of them to four males: Vega, Balrog, Gen and Yun (Arcade Edition only). Out of the other girls, only Ibuki and Sakura play it straight in Ibuki's route: Makoto fights Fei-Long, Sakura doubles as Dan's rival, Rose both has Ryu as her rival and is one of Guy's possible rivals (the other being Cody), and both Juri and Viper can have male rivals too (Bison, for Juri; Hakan, for Viper).
Originally averted by the old Smackdownvs Raw games, which allowed male on female matches and even had an 'undetermined' gender to allow characters to win both male and female titles. One entry in the series actually had a challenge mission that tasked the player with using Candice Michelle to defeat The Great Khali. Unfortunately the series has succumbed to political correctness in recent years and the the only match type that can feature both males and females is the mixed tag match. If you are controlling a male character then the game makes it almost impossible for you to strike a female competitor and you are forced to tag out. If you do somehow manage to land a blow then you automatically lose the match by DQ.
Averted in Sonic Riders, in which Tails's rival, Wave, is female.
Webcomics
Mostly averted in The Order of the Stick as males in the comic are willing (and in some cases, more than willing) to take on female opponents (Belkar vs Hag, Roy vs Sabine, Roy vs Miko, Belkar vs Miko, Hinjo vs Miko, Redcloak vs Miko, everyone vs Miko, notice a pattern here?). However, Haley has noted that she has a tendency to end up fighting flying, murderous skanks. She even cracks a line that Leeky's Animal Companion was likely some sort of bird-hussy.
Problem Sleuth: Hysterical Dame and Nervous Broad are the ones who fight and defeat Madame Murel; all three are the Distaff Counterparts of Problem Sleuth, Pickle Inspector and Mobster Kingpin.
Averted in The Law of Purple, as most guys have no problems hitting girls.
In the TGWTG Team Brawl Spoony made The Nostalgia Chick fight That Chick with the Goggles while he would take Bennet the Sage. As Nostalgia Chick and That Chick with the Goggles fight Spoony and Bennet simply grabbed their cellphones and started taking pictures.
Thoroughly averted in Red vs. Blue, where virtually all of Tex's battles have been against men.
Epic Rap Battles Of History. The only boy vs. girl battle they've done (Adam vs. Eve) ended with the two making up and going for lunch. The only other two battles with females have been girl-on-girl (Palin vs. Lady Gaga and Cleopatra vs. Marilyn Monroe).
Western Animation
Heathcliff And The Catillac Cats had an episode featuring a female opponent for Heathcliff, Terrible Tammy, who tried to take over Heathcliff's territory. He couldn't hit her, but his otherwise ladylike girlfriend Sonja didn't mind beating her up.
Generally averted, but in one of the earliest episodes, the only girl of the hive (Jinx) fights one of the two girls of the team (Raven). Even though there were two girls, Starfire was helping Cyborg at the time. Possible Lampshade Hanging from this quote from Jinx: "You fight like a boy!"
Jinx is Raven's Shadow Archetype, so they end up fighting whenever the groups battle anyway.
When Trigon makes Evil Counterpart to three of the Titans (including Starfire) this looks to be the case as they fight their own mirrors, but then they do a Rock Paper Switch.
The two-parter origin episode for Two-Face in Batman The Animated Series had Two-Face's fiancee step out of her Neutral Female role to attack the mob boss's one female minion, who was about to underhandedly enter the battle with the guys herself.
The big reveal flashback has Batgirl stay behind to battle and then chase down a fleeing Harley Quinn, leaving a tortured and psychotically broken Tim Drake behind while she gave chase.
Harley Quinn gets into a particularly brutal fight with Mercy Graves, Lex Luthor's female bodyguard during the crossover with Superman The Animated Series. She later tapes up and gags Mercy as a bit of payback, but in the end, it's Mercy who has the last laugh. Literally, since she laughs her butt off while watching Harley getting hauled to jail.
The Batman made its version of Poison Ivy significantly younger than her comics counterpart so that she would be the same age as Batgirl. Her first appearance was in Batgirl's introductory episode and any time she shows up as the villain of the week, it is typically a spotlight episode for Batgirl.
In the Justice League episode "Secret Society part II" The JL and Gorilla Grodd's Secret Society battle in a football stadium. Superman is about to punch Giganta (who in this version is more girly than the Super Friends version) but hesitates when she pulls the "You wouldn't hit a woman would ya?" line. Behind Superman, Wonder Woman answers "I would!" flying in and knocking Giganta out.
It was invoked in the later episode 'Grudge Match', in which the villainess Roulette was having difficulty attracting spectators for her underground superhuman fight club. She got the idea to abduct superheroines, and brainwash them into fighting each other in order to draw the crowds. The episode culminated in Hawkgirl, Black Canary, Vixen and Huntress all trying (and failing) to pacify the still-brainwashed Wonder Woman.
Basically any Toyetic animated cartoon from the 1980's that had a female team member on the good guys' side had a counterpart on the opposing team. This was particularly apparent in the show Visionaries which had people who could temporarily turn into magical animals. Galadria of the heroic Spectral Knights turned into a dolphin, and thus the only villain she could fight was Virulina of the evil Darkling Lords, who turned into a shark.
Galaxy Rangers managed to be an aversion most of the time, despite having a female Big Bad and several Action Girl characters among the guest cast and Rogues Gallery. The notable exception was in "Scarecrow's Revenge" where the titular villain turned Maya Brainwashed and Crazy and sent her against Niko. The scene's almost a punchline in the fandom, as Maya had been hitting on Goose earlier.
In the Mega Man cartoon, one episode had Roll attacked by a female cosmetics robot who gave her a bad facial. Megaman gave the robot an equally bad facial with a tube of makeup, and offered to fight her, but Roll insisted that she handle this.
Season two largely subverts it. The good guys team is two boys and one, later two girls. The evil team is female-only. So the good guys have to hit girls. But Sokka and Aang have no problem with that as long as they are dangerous girls.
Played with and justified during the Grand Finale. Zuko and Azula end up in an Agni Kai and he almost wins but Katara is the one who ends up defeating her.
Played straight when Azula, Mai, and Ty Lee attack Suki and the other Kiyoshi Warriors even though they're all female. Ty Lee even tells them that they're not prettier than them. The next time Suki runs into Azula and Ty Lee at the Boiling Rock, she looks forward to the rematch since it's personal.
The Pac-Man cartoon had Pac-Man and Ms Pac-Man as the good guys, and four male ghosts and one female ghost as the bad guys. Guess who fought whom?
Because Popeyewon't hit a woman, he's always a bit helpless against a female antagonist. Olive is perfectly willing to step in and clobber them, though, with a little spinach boost.
Real Life
Odd Truth in Television: Lions. If an alien lioness wanders into another pride's territory, the pride's females will attack her, while the male(s) watch and do nothing. If a strange male comes in, it'll primarily rely on the pride's male(s). The females often get involved because if the male stranger wins, they'll have to say bye-bye to their cubs.
It's Truth in Television for most actual martial artists. Most tournaments are divided by age, rank, and gender. Classes, too, for the most part, will try to partner girls with girls during drills and sparring matches. It's done because a) it eliminates a biological strength advantage, and b) sparring and grappling with an opposite gender opponent you don't know well can be very awkward.
In competition, it's true that most tournaments are divided by gender, just like almost all sports. In drills and practice sparring, it depends on the martial art and individual school. Some martial arts don't depend as much on either grappling or strength, so there's little reason to segregate opponents by gender.
Another reason for gender division in tournaments is lingering gender bias. A female competitor is more likely to accept losing to a male counterpart. If the guy loses they tend to sulk over the idea of losing to a girl.
Schools that focus more on self-defense avert this with sparring, figuring that a woman should know how to handle herself against a larger man.
When observing the fighting behavior of vervet monkeys, Cheney and Seyferth witnessed an incident that fits perfectly: Two male monkeys (call them Albert and Bob) fought with each other. Twenty minutes later, the revenge came in the form of Albert's sister suddenly attacking Bob's sister.
