Ahn Ok Yun (Jun Ji-Hyeon), the sole female assassin in the 2015 South Korean film Assassination.
Leigh (Laurie Zimmer) in John Carpenter's original Assault on Precinct 13 (1976). She starts out as just a secretary in a police station but becomes an action girl when the nearly-abandoned station is under siege by a street gang during the night and fights them off along with the lone policeman and two convicts. She keeps her cool especially in comparison to the other secretary who panics.
Barely Lethal revolves around Megan, a teenage girl assassin who fakes her own death so she can go to high school.
Francesca Bruni in 2005's Casanova. Your brother is a poor swordsman who's got himself into a duel? No problem, just take his place and kick ass!
Kyra has developed into one by The Chronicles of Riddick, beating up various men larger than she is, evading an alien helldog, and even holding out against the Necromongers for a while.
Pam Grier's title character in Coffy from 1973 was one of the first full-fledged examples, and probably the first black one.
Valeria (Sandahl Bergman) from Conan the Barbarian (1982). Took lessons from master Kiyoshi Yamazaki who worked with Schwarzenegger and Lopez. Swung a sword, looked good doing it.
Lynn Redgrave's character Mary O'Donnell in Don't Turn the Other Cheek! single-handedly comes to Russian conman Dmitri and Mexican bandido Max's rescue by beating down about ten or twenty of Huerta's soldiers with her bare hands.
Rookie Judge Cassandra Anderson in Dredd proves herself to be highly capable over the course of the movie. Not only does she mentally kick Kay's butt multiple times, but she rescues herself when she gets captured, saves Dredd from the corrupt Judge and even stands up to Dredd with regards to the fate of the Clan Techie. It's no wonder that Dredd gives her a pass at the end of the film.
Maya from Eight Below. Only female dog and the leader of the pack.
"The Mountain Girl" from D.W. Griffith's Intolerance is one of the earliest, if not the first, film example. She is a Babylonian who isn't particularly interested in romance but likes eating onions and killing Persians. When the Persians attack and she takes to the walls with the rest of the army to fire arrows, she enjoys herself.
Johnny Mnemonic has Jane, a female cyborg bodyguard. She's not as Badass as Molly Millions in the original story, but this was probably due to the limits of cinema at the time.
Claire from Jurassic World is this trope played in a rather interesting way. As she's the park operations manager, she's hardly an athlete or a trained fighter, but she is a very intelligent and determined survivor, so when she gets a Moment of Awesome, it comes from her wits rather than any physical prowess or training. Despite this, she still saves Owen's life from a Dimorphodon which was attacking him by clubbing it with a tranquiliser rifle and then double-tapping it, and she manages to outrun a Tyrannosaurus Rex while in high heels.
Beatrix Kiddo in Kill Bill. Trained by one of the greatest warriors to ever live, she was a professional assassin and is considered the deadliest woman in the world. She single-handedly cuts her way through almost 88 sword-wielding bodyguards before going on to dispatch an entire team of highly-trained assassins in her Roaring Rampage of Revenge. The other major females fall into Dark Action Girl territory.
In Last Action Hero, Slater's daughter is one of these, and at first it's played for laughs by subverting the Distressed Damsel — she's screaming mock-hysterically as she kills the mook sent to take care of her. But it's also deconstructed a bit when Slater mentions that she spent her prom night alone in her room, field-stripping an AK-47.
In the first film, Arwen Evenstar carries a wounded Frodo from Weathertop to Rivendell, outrunning the Black Riders.
Imperator Furiosa from Mad Max: Fury Road. She's a Badass Driver who leads several of Immortan Joe's Wives to keep them out of a constant life of sex slavery. She's also an incredibly good shot and physical fighter, even handing Max his ass several times. A number of critics and fans have begun to call her this generation's Ellen Ripley.
Miss Piggy turns into an Action Pig in numerous Muppet movies. You mess with the frog, you will get hurt.
Saga in Mitt liv som hund (My Life As A Dog). She beats all the boys at boxing and is the best on her all-boys' football (soccer) team.
Red Dawn (1984). Teenaged girls Toni and Erica, who subvert the usual trope by being too rugged up in the Colorado winter to be much fanservice. After the Ragtag Bunch of Misfits kill their first Dirty Communists, they state flat out that the guys can do their own washing up. We later see them blasting away in ambushes and using their feminine wiles to get bombs into places where the Russians really don't want them going off.
Interesting little semi-subversion in Red Eye. Rachel McAdams' character is manipulated, abused, and (metaphorically) raped by Cillian Murphy's Magnificent Bastard, and eventually she decides to man up (for want of a better term) and brutalize him with a pen, a shoe, and a field hockey stick. She does pretty well (or at least, well enough not to be a Faux Action Girl), but she still needs the help of Daddy Brian Cox, who also mans up just in time.
In the third Riddick movie, Dahl (Katee Sackhoff) is a seasoned mercenary and sniper, and beats up an attempted rapist.
The women of Old Town in Sin City, as they have to rely on each other for protection from rowdy customers.
Princess Leia Organa from Star Wars often switches in and out of the Action Girl role. She must have got it from her mother, Padme Amidala, who is, incidentally, the best shot with a blaster in the entire series.
Rey in The Force Awakens. The first time Deuteragonist Finn sees her she hands two assailants their asses using nothing but her staff. That's just the tip of the iceberg really, since she also turns out to be an Ace Pilot capable of flying the Millenium Falcon just as well, if not better, than Han and Chewie. She's a good shot too. Most importantly however, she's also The Hero of the film - effectively the new Luke Skywaler - since she actually has a strong connection to the Force and is larval Jedi-to-be, resulting in her beating Kylo Ren in a lightsaber duel in the film's climax.
Selena in 28 Days Later has this kind of scheme going on. Since 28 Days Later is on the cynical end of the Sliding Scale of Idealism Versus Cynicism, she may be badass and violent, but she's still just a rather athletic chemist with a machete. It's therefore understandable when she gets a bit Chickified toward the end when surrounded by a bunch of soldiers.
Gwen Conliffe from The Wolfman (2010) eventually becomes the Victorian equivalent of this when she becomes so motivated by trying to save Lawrence that she totes a gun around while running around in a dark forest in the middle of the night — certainly breaking the Damsel in Distress version of her character from 1941.
Blink's powers make her extremely effective in fighting the Sentinels, both in taking them out herself and assisting the others in fighting them.
Mystique is the only mutant back in the past who's been doing anything for the last few years (Magneto's been stuck in the Pentagon for a decade, and Xavier's been moping around the house since the start of the Vietnam War.) Even once the plot takes off, she's arguably the most active character.
Yukio introduces herself in a bar brawl and proves competent enough to protect Logan. And later helps him fight Viper.
Mariko is proficient in softhanded martial arts and an excellent knife-thrower, helping to kill Silver Samurai.
Franchises and creators with large bodies of Action Girl work:
Action Girls were not common in early movies, as the true form usually requires convincing hand-to-hand combat skills. However, a female character in a Western or Pirate movie could get away with the role. Maureen O'Hara is probably the most famous. She had a powerful screen personality, great acting skills, and an ungodly beauty that could carry any part. She also always looked to be having enormous fun whenever she got in a swordfight, most particularly in Against All Flags (as a Pirate Girl) and At Sword's Point (as the daughter of one of The Three Musketeers!).
Marybeth from Hatchet is a deadly shot with a gun and never backs down from a fight against Victor Crowley.
Sydney Prescott from the Scream films always stands up to the killer at the end of each movie, and truly grows into the role in Scream 4, where she actively hunts down the killer and fights them with confidence.
In Aliens, Ellen Ripley was slowly converted from a Final Girl into an early example of the Action Girl. Her performance earned her an oscar nomination and the number 8 spot on the AFI's Greatest Heroes list. She frequently appears on lists of the best female Heroes. We also see Vasquez, a butch action girl.
In the first two Terminator films, Sarah Connor grows from Distressed Damsel to one of the most badass heroines of all time, perhaps the only other that can truly stand beside Ellen Ripley.
Mace in Strange Days. It pretty much takes an entire police SWAT team to kick her ass. Justified in that she's a professional bodyguard, whom you'd reasonably expect to be able to kick someone's ass if necessary.
Most recently, in Avatar we have Trudy Chacón who goes out all guns blazing, the Na'vi princess Neytiri and — while not quite an Action Girl in this film — Sigourney Weaver's Dr. Grace Augustine, who's still no Distressed Damsel.
Many Kung Fu movies. In particular, characters played by Cheng Pei-Pei (60s and 70s), Brigitte Lin, Michelle Yeoh (both 80s and 90s; coincidentally, she played the aforementioned Wai Lin), and now Zhang Ziyi.
Yeoh, Zhang and Cheng came together as Shu-lien, Jen, and Jade Fox of Crouching Tiger, Hidden Dragon. The sequence in the bar is FANTASTIC, as well as the fight between Shu and the rebel Jen.
Thai actress Jeeja Yanin has also made a name for herself in martial arts movies in recent years, starring in films such as ChocolateRaging Phoenix, and Jukkalan (a.k.a. This Girl is Badass)
In the 1980s, the so-called "girls with guns" subgenre took off in Hong Kong action cinema. Despite its name, the "guns" in question were usually quickly discarded in favor of bareknuckle brawling, thus making more straightforward Action Girl stars out of Michelle Yeoh, Cynthia Khan, YukariOshima and Cynthia Rothrock. The latter two were actual martial artists (and Oshima was also a stuntwoman), making this borderline Truth in Television.
Tony assembles the Mark 42 around Pepper in one scene, which she then uses to save Tony. Pepper also gets injected with Extremis later, allowing her to save Tony from the similarly super-powered Killian.
Mothra has been the Kaiju version of an action girl since her first appearance, and is arguably one of the most successful ones ever, starring in her own film series, and appearing frequently in the Godzilla franchise. In the case of the latter, she's one of the few monsters to ever defeat Godzilla (and did it with no fancy powers), is willing to stand up to King Ghidorah in her larva form, and usually takes on the role of The Smart Guy and Only Sane Man during team-ups.
The Hunger Games: Katniss Everdeen has been the breadwinner in her family since her father died, and was a talented hunter even before that. She's lethal with a bow and when she enters the Hunger Games, she puts those skills to use. She quickly proves herself to be formidable, intelligent and determined. She manages to beat out other competitors that are not only physically stronger and working together, but whom have been training their entire lives to kill.