Black Canary is a character who fluctuates between Action Girl and Faux Action Girl, depending on the writer. Chuck Dixon and Gail Simone, in Birds of Prey, were frustrated at the fact that she always seemed to end up as a victim/hostage, and devoted much of the comic to re-establishing Canary's Bad Ass credibility. Sadly, the Green Arrow/Black Canary title utterly evaporated all that martial arts street cred.
Just about every female character from the Dreamkeepers 'verse qualifies for this trope in some way.
Ivy Raven, operative of the NSB, is the go-to agent whenever something needs to be tracked down, hushed up, or gotten rid of in the Echo universe. Unless your yourself have access to a high-tech combat suit built of unobtainium, you should stay out of her way.
Sue Storm! She sure started out as a Faux Action Girl, but man did she ever level up. She's now the toughest fighter on the team, and she's on a team with Ben Grimm!
It's a bit more complicated than that. She's the most powerful person on the team, but that doesn't necessarily mean she's the most ruthless or skilled fighter. If she's aware of a threat and willing to cut loose, she can kill with a thought, but she'd much rather create barriers to protect her friends or restrain her enemies.
She defeated The Hulk alone - not even Ben Grimm has been able to do that. When she fought Wolverine in his own book, he turned tail and ran because she had his number. Sue wins.
Scarlett in the G.I. Joe comics, followed closely by Lady Jaye and even Cover Girl.
Gotham Central has a cast split almost 50/50 between male and female police officers, and each and every one of the women is an action girl (At least, we are told they are. Some simply never get enough time in the spotlight to confirm or deny these findings). Being cops they have to be, especially since they regularly deal with supervillains that fight Batman, and thus have to be Badass Normals in their own right:
Detective Romy Chandler is probably given the first real action moment. Having discovered the secret identity of Firebug and trapping him within the police station, Firebug activates a hidden flamethrower to burn his way out; however, instead of burning Nate Patton to a toasty crisp, he is instead instantly buried in foam. The next panel shows Romy standing there, holding a fire extinguisher and glaring at him.
Renee Montoya gets the next reveal of her action potential. Apart from "minor" incidents throughout the series (Like beating the crap out of a rapist when he starts following her with a video camera) she gets to beat up a few "freaks" (supervillains) singlehandedly, starting with Two-Face. He has ruined her life (Framed her for murder, outed her to friends and family, kidnapped her, etc.) and is now holding her prisoner, but she knocks him down and goes right after his gun, and she does not stop until the Batman himself shows up.
Montoya built up enough of a reputation that she became the new Question when Vic Sage died.
Modesty Blaise, whom Jennifer K. Stuller (author of ''Ink-Stained Amazons and Cinematic Warriors: Superwomen in Modern Mythology) called "The most complex, sophisticated, skilled and intelligent of all action heroines".
Elsa Bloodstone, to stupidly ridiculous proportions, kicking the ass of anything with an ass using anything from shotguns to shovels to guitars.
Elena Kurakin, a half-Mongolian swordswoman and Rudinshtein Irregular who killed her commanding officer for cowardice in Nikolai Dante.
Nth Man: The Ultimate Ninja has Colonel Vavara Novikova, head of the KGB's Spetsburo (Assassination Bureau) and the second-deadliest assassin on Earth.
In Steve Gerber's Omega The Unknown, one of the protagonist's surrogate parents fits this bill, being a savvy New Yorker living in Hell's Kitchen who makes money by following supers around and taking pictures of their battles for JJ Jameson, who she then argues with about compensation.
Painkiller Jane is a female version of the Punisher. In fact she even slept with him in a crossover. Her friends the 22 Brides are all experts in guns and killing things as well.
The Rat Queens, the titular mercenaries/adventuring party from the eponymous comic book, are a party of these. Approximately 50% of all of Palisade's adventurers are women, including one all-woman group, one group with three women and one man, and one group with a single woman and three men. The only group without any women in it is the Four Daves, an all-male group where, you guessed it, every member is named Dave.
For all the Hubbub about how sexist Starfire was in Red Hood and the Outlaws #1, people seemed to forget she took out a group of tank armed with 38 mm canons that give both Jason Todd and Roy Harper(two very dangerous men, who just slaughtered a prison's worth of armed military guards with two pistols and a bow.) pause, with almost no effort in the same issue. In fact beside being jumped by Crux and having her powers temporarily zapped in the currently 10 issues of RHaTO it's hard to find a time when Starfire isn't kicking someone/things ass. She no longer boast about being an Okaaran Warrior, she shows she's an Okaaran Warrior.
Rebel commander Mirith Sinn. She joined the Alliance after her husband was murdered by Darth Vader to make a point, and rose through the ranks until she in charge of a base on an Outer Rim world. And she is not shy in the least about getting her hands dirty. When things get desperate, she charges to the front lines, coldly dispatches Imperial guards, and even allows herself to be captured and tortured so an ally can escape. She even withstands the torture no matter how painful it got—until the enemy commander began an orbital bombardment of her troops' fallback position.
Midnight from the Teenage Mutant Ninja Turtles story arc "Body Count" is a great example of a Badass Normal action girl; she is one of the best fighters in the story, able to beat a 300 pound giant of a man in unarmed combat and is pretty useful with guns and swords. It is worth noting that she was based off Kevin Eastman's wife at the time Julie Strain.
Kitsune does not exactly qualify (preferring stealth to more direct approaches), but has been shown to have some skill with swords/battle tops/knees...
Also some minor characters, like Saiko the assassin.* Tara, Mariah and Shakira from The Warlord.
Action Call Girl in the case of Gail, one of the more badass girls of Old Town, and Dwight McCarthy's Warrior Woman.
An unnamed miller's daughter in a story by Wilhelm Busch. She's alone when three robbers enter the mill, one of them implied to be a rapist. But without feeling in trouble for a moment, she flattens the wannabe rapist with a millstone, rolls up the second robber to a spiral (with the help of the turning axis of the mill-wheel), and beheads the third one (who apparently doesn't care for the fate of his mates) when he tries to rob the gold from a chest. The author comments: "This is how one single girl gets three men into trouble." Read it here.
The archetypical comic book Action Girl is, of course, Diana Prince a.k.a. Wonder Woman, created for just that purpose in 1941. Not the first female superhero, but a true cultural icon and never out of print in 67 years. (Since until recently, if DC didn't keep making it they would lose ownership).
Every X-Woman in existence has had an Action Girl moment, but doubly so if she was created/handled by Chris Claremont. Notable Action Girls include Storm, Psylocke, Polaris, Rogue, Emma Frost, X-23, Domino, Kitty Pryde, Dazzler, Jubilee, and Jean Grey. Though special mention goes to Storm, who led the team without her powers during a long period in the '80s, and accumulated several Badass levels during that period.
Plourr Ilo. Just look◊ at her! She is a princess and her story is loosely based on that of Anastasia, but she is also a competent mechanic and pilot, a bit of a Tsundere, and both strong and good at hand-to-hand combat.
The Bat Family has a record of having some of the most awesome Action Girls (Barbara Gordon both as Batgirl and Oracle, Cassandra Cain as Batgirl, Spoiler, Huntress and Catwoman, just to name a few) and tending to go through long periods where those girls are Stuffed In The Fridge or misused in some other way, before making returns.
Every superheroine ever has this as a part of the job description.Well at least look like it.