Brienne of Tarth from A Song of Ice and Fire is arguably a mix of Action Girl and Failure Knight. A talented warrior (in a fairly patriarchal fantasy society) who watches the man she loves get murdered by a shadow and still tries to defend him. She also manages to defeat many skilled knights (often outnumbered) and is doing pretty damn well on her quest before being hanged for a traitor. Some people have no luck.
The series also contains Asha Greyjoy, Meera Reed, Osha and Ygritte, all who play this trope fairly straight without Brienne's terrible luck. Though, poor Ygritte did have the misfortune of getting sacrificed at the altar of Jon's Woobiedom.
Arya's journey of survival across Westeros cemented her Action Girl status before she turned eleven.
There's also Oberyn Martell's bastard daughters, the "Sand Snakes," whom Oberyn has raised be strong and fend for themselves. At least one, Obara Sand, is a trained warrior, and her sister Tyene is an expert on poisons. Action Girls have something of a tradition in Dorne, since their legendary Queen Nymeria was said to be a great warrior.
House Mormont of Bear Isle also has a history of producing female warriors, since they needed to defend themselves from Iron Island raiders while the men were away fishing. Lady Maege Mormont and all five of her daughters are skilled fighters.
When Aegon the Conqueror began his conquest of Westeros, he was accompanied by his sister-wives, Rhaenys and Visenya. Visenya would commonly braid her hair and dress as a warrior, wielding the Valyrian steel sword Dark Sister in battle and ride the dragon Vhagar. Rhaenys, the more feminine and playful sister, rode the dragon Meraxes in battle alongside her siblings.
Since ASOFAI is in many ways built upon Deconstruction of fantasy literature, Martin makes quick work of subverting this trope for all its worth, as it by now so much as an obligation for a fantasy series to include it. Some Action Girls, like Brienne and Arya, have to fight their culture to show their strength in battle...becoming part of War Is Hell and using so many Determinator points it leads them to near-trauma and de-humanization. Asha is particulary jaded, as she comes from a very chauvinist culture and has to work a lot to pull it through. Other Action Girls come from more permissive cultures, like Osha and the Mormont girls, and thus are more natural about it.
In the markets of Vaes Dothrak, Daenerys takes notice of warrior maids from Bayasabhad, Shamyriana, and Kayakayanaya, who wear iron nipple rings and rubies in their cheek.
Another action girl in the series with poor luck is Pretty Meris, a female mercenary belonging to the Windblown company. Supposedly she was raped by half the members of a different mercenary company. She has a severely scarred face and is described as being anything but pretty.
In Battle Royale, there is Takako Chigusa who takes out Kazushi Niida, who plays football and is well built, by gouging out his eyes and thrusting an ice pick down his throat. There's also Mitsuko Souma, who acts like she is weak and helpless but is actually participating in the game and has taken out quite a few of her classmates intentionally, and Yukie Utsumi, who was hiding out in a lighthouse for the majority of the game and could have survived had it not been for Yuko, who tried to poison Shuya's meal after witnessing him accidentally killing Tatsumichi Oki, only for it to backfire with devastating consequences.
Also Noriko Nakagawa. Even though she is pretty much sidelined from most of the action, she manages to take out, of all people, Kazuo Kiriyama.
Mearad of Pellinor from Allison Croggon's Books of Pellinor series is a swordswoman and warrior. Sylvia of Innail could also be considered an action girl since she's seen battling the mountainmen in book four.
Jame of P.C. Hodgell's Chronicles of the Kencyrath?a martial arts expert, formerly a professional thief who pulled off some of the most impossible thefts, and in training to be a military officer.
Par for the course in the Ciaphas Cain novels, given that a bulk of it takes place during the titular HERO OF THE IMPERIUM's time in a mixed-gender ImperialGuard regiment. Aside from commanding officer ColonelKasteen, recurring characters include cheerfully sociopathic Mari Magot, perpetually unlucky (but still perfectly competent) "Jinxie" Penlan, and future Lady General Jenit Sulla.
Karrin Murphy with (particularly in early books) a bit of The Lancer thrown in. As she is the Badass Normal, she can have trouble with some of the things that she has to face, but after a while, she learns the rules for battling things, and kicks ass.
The Lancer disappeared in the recent books, as Murphy begins to out-badass everyone in every book. Including Harry.
Susan Rodriguez, after she was turned demi-vamp in Grave Peril and joined the Brotherhood of St. Giles against the Red Court.
Miss Gard. A Valkyrie with a penchant for firearms.
Lara Raith at times. She's The Vampin every sense, but she's also quick to kick ass when need be. She takes the lead and guards the rear in a super-ghoul attack, even if she does have to be badgered into it by Harry, and in a later book she arrives on the battlefield by jumping out of a helicopter, and eats her cousin while on fire.
Charity Carpenter. Spars with her husband (a master swordsman), makes his weapons and chainmail, and helped Harry assault Arctis Tor, Mab's personal fortress.
Badassery is inherited. Molly is noted to be an absolute terror with illusion magic. 'One Woman Rave' indeed.
Gaia Moore from Fearless has extreme physical prowess, is heavily trained in martial arts, has an extremely high IQ, and a defective physiology because she can't feel fear. And she routinely goes looking for asses to kick.
From Gail Carringer's Young Adult Finishing School Series the protagonist Sophronia Temminnick becomes one after enrolling in a manners/espionage school. The overwhelming majority of the students there and all the female instructors are action girls as well.
The titular character in Robert Heinlein's Friday epitomizes this trope. She is stronger, faster, smarter, and hornier than everyone she meets. Most of Heinlein's heroines are larger-than-life, but Friday is literally superhuman.
Deety in The Number of the Beast is a 22 year old busty strawberry blonde who is a precocious super-genius polymath with a PhD, a crack shot, and an expert martial artist.
Lana, Dekka, Brianna, Taylor, Penny, Brittany in the Gone series...it would be easier to list the exceptions (Astrid, Mary, and Diana), though even they have their moments. As of Fear Astrid definitely counts as a full on Action Girl.
Sarah from Greystone Valley...or at least she seems to be on her way as the story progresses.
Tonks is also implied to be a skilled witch (Auror training is difficult, and you'd have to be badass to have Alastor Moody as your mentor), though we never really see much of it.
If Katniss Everdeen of The Hunger Games wasn't this before the title event, she is by the end of them.
Johanna Mason. Also, any female Careers.
In Death series: Eve Dallas is very much this. Peabody tries to be one, even though she is nowhere near Eve's level.
Arya of Inheritance Cycle, who reminds Eragon of this whenever he expresses concern over a danger to her, and seems to disdain "helpless females" who aren't. Christopher Paolini mentioned once that just about every good story has an Action Girl.
Llana of Gathol, from John Carter of Mars. For its time, this was an extremely daring thing to do.
Even more so Tavia, the heroine of A Fighting Man of Mars.
Judge Dee operates in Imperial China where Confucian ideals place women firmly in the home. Never-the-less he manages to encounter at least two Action Girls in Miss Violet Liang, a Mongolian woman-wrestler, and Blue-White, a skilled street fighter.
Kate Daniels has a Cool Sword and throwing knives, and she is quick to use them. Her best friend Andrea is deadly with her guns. This is only to be expected in post-Shift Atlanta, when monsters prowl the streets and nobody is completely safe.
Private investigator Kate Shugak is 5 foot 1 inch tall, carries a scar that runs from ear to ear across her throat and owns a half-wolf, half-husky named Mutt. Orphaned at eight years old, Kate grew up to be resourceful, strong willed and defiant. She is tougher than your average heroine - and she needs to be to survive the worst the Alaskan wilds can throw at her.
Kindling Ashes: Giselle grew up in the streets and so she knows how to scrap, but against an older person with greater strength and experience, she escapes instead.
Lucy Pennykettle from The Last Dragon Chronicles. Once the Shadow is taken out, she reverts back to Lucy while still retaining her knowledge on how to kick butt.
Teotl, Shahmeran, and Blackthorn in the League Of Magi stories are all bruisers in their organizations.
Catti-Brie, of the Drizzt novels, is a reasonably competent Action Girl. This is helped by her truly badass equipment; her sword would be decent equipment on someone four times her official character level, and her bow is all but epic. She even beats Drizzt in sparring matches now and again, and he's fifty years her senior, still in his prime, and trained since his youth to fight. However, a recent wound to the leg that didn't heal right lead her to taking up magic. After three books of this, she died in the Spellplague..
In game terms, though, it's noteworthy that she has the lowest character level of any of the Companions of the Hall — Drizzt is 16, Bruenor is 12, Regis and Wulfgar are both 9, and Catti-Brie is (before her magical training 4). She does, however, have the least overall combat experience, so this is justified.
Salvatore's other leading original Forgotten Realms female, Danica Maupoissant, is also a warrior. In her case, she's a fighting monk, trained from her youth both in unarmed combat and the use of some very fine knives, and by the second book of The Cleric Quintet the foremost student of a long-dead grandmaster's teachings. She's skilled enough to fight alongside and impress centuries-old elven warriors before she's even thirty. She's skilled enough that she's capable of briefly holding her own against Artemis Entreri, top it off with the fact that he had his weapons and she had none.
The Seven Sisters from the Forgotten Realms all fit the template to some degree.* Huang Rong and Mu Nianci, from Legend of the Condor Heroes.
In addition, and Myrmidon in the same series. Special mention to Feyt.
Clarissa Kinnison (nee McDougall) of E. E. “Doc” Smith's Lensman novels, and all four of her daughters. Arguably Virgilia Samms from the same universe, in as much as she's an integral part of Triplanetary's senior operations planning and is as exposed to danger as any of the men (to the point where she's captured and tortured, and barely escapes with her life). In Masters of the Vortex, there are several female members of Neal Cloud's crew who kick MAJOR arse, including the epic scene where they commandeer the weapons Cloud was issued for use as overclocked drilling and sampling lasers, and reduce the local gangster boss's fortress to a puddle of boiling rock along with everyone in it. The Lensman universe was pretty much Smith's redemption for making Dorothy Seaton such a shrinking violet for all but the very last part of the Skylark Series. Clio Marsden in Triplanetary doesn't fight anywhere near as effectively as her male compatriots; but given that she starts the story as a naive young civilian, she doesn't do too badly.
Several in Nightrunner, considering one of the major settings is a matriarchy with lots of women warriors. Most notably Beka, the princesses Klia and Phoria, and Retired Badass Thryis.
Elsabeth Soesten of the fantasy novella No Good Deed.... She's a skilled swordswoman in her own right, who infiltrates an abbey by spelunking its privy shaft, and can take out an assassin moments after awakening from a drunken daze. Crosses over with Action Survivor as she just as often escapes by pure luck or because someone is manipulating everything behind the scenes.
Nearly all the women in Gail Dayton's One Rose Trilogy. Certainly all the women in the Varyl ilian.
Both parts of Phantom's Reckoning give us two. In the first one, we have Alice Clair, a BadassTsundere with fire powers, and Layla Thompson, who uses electric powers and upon her first appearance in the story tried to take on the Phantoms all by herself. The second part gives us Makoto Guererro, a Tomboy who lives on the streets along with Tatsuya, and also has electric powers, and Kaori, a Combat Medic with ice powers. The first one had more standard warrior type action girls, while the second had more typical teenager figures who got the Call to Adventure.
Kyri Vantage in Phoenix Rising. Carries a greatsword that she uses to great effect, climbs mountains, and Guild Adventurer set on a vehement vector of vengeance (and justice).
Michael Scott's The Secrets of the Immortal Nicholas Flamel series is full of them. Perenelle Flamel is a powerful sorceress, Scathach is an ancient Celtic warrior and Sophie takes a level in badass when she gets her magical powers activated. Then none other than Joan of Arc shows up in the second book.
Septimus Heap: Many women in the Septimus-verse qualify, including Marcia Overstrand for fighting with DomDaniel about the Akhu Amulet in Magyk and Jenna Heap for knocking down the Toll-man in Queste, among others.
Milla of the Far Raiders of The Seventh Tower is tougher and more physically competent than any fourteen year old should be... on the other hand, she is still a fourteen year old, and behaves like one, behaving in an incredibly arrogant and at times almost homicidal way towards Tal in the early book. She grows up a lot as the series continues, like Tal, mostly due to common sense being drilled into them both by reality.
The Shannara franchise has had a few. While the original trilogy was lacking in this department, The Heritage of Shannara featured Wren Ohmsford, and Matty Roh, both of whom were perfectly capable of looking out for themselves and kicking major ass. Wren fought her way in and out of Morrowindl using a knife and the Elfstones, while Matty is a Waif-Fu abusing, rapier-armed Broken Bird who can match the Federation's best, and cheerfully goes after The Shadowen using only her sword. The Voyage of the Jerle Shannara also has two, in Tamis (Elven Hunter, personally trained by the Captain of the Home Guard), and Rue Meridan, who at one point jacks an entire airship by herself.
David Isaak's Shock and Awe features multiple examples of this, most notably the heroine, Carla, who is probably the most realistic, believable portrayal of an action girl ever seen.
Pity from the Sinister Six Trilogy is able to roll with the rest of the Sinister Six and go toe-to-toe with Spider-man all by herself.
There's a fair amount of them in Skulduggery Pleasant, most notably Valkyrie Cain, the main protagonist; Tanith Low, agile swordfighter; and China Sorrows, information broker.
In Melisa Michaels's Skyrider series, Melacha "Skyrider" Rendell is a taciturn, two-fisted hot-shot belter pilot who likes to get into fist-fights to perk herself up after a dull run. Or to relax after an overly exciting one. Or because it's Tuesday. Really, who needs an excuse?
Most of the main female characters in Spaceforce qualify. Jez because she's a bad-ass space cop, Ashlenn because she's a bad-ass Proud Warrior Race Gal and Mizal (even though she's dead) because she's a bad-ass secret agent.
In Spider-Man: The Darkest Hours, during Spider-Man's fight with The Ancients, Mary Jane beats the crap out of the last Ancient with a tire iron while quoting Macbeth. She's also saved Spidey more times than he's saved her, beaten up like a million stalkers, & was trained by the epitome of Manliness Captain America, If that's not Action Girl, what is?
And in Spider-Girl, she not only faced Normie Osborn aka the third Green Goblin, but actually shames the boy via a nice "The Reason You Suck" Speech. ("I used to change your diapers, what makes you think I'm scared of you!?")
Aunt May too, Look up how she delt with Chameleon in the Civil War, do it.
Then there's Jaina, who is at once Badass enough to take down one of the most powerful and yet least impressive Sith Lords ever, her twin brother nonetheless, and yet despite being a fully-functioning Jedi Knight and part of the Skywalker line (which practically burns with Force potential), had to get additional training from Boba freaking Fett, a seventy-year-old cancer-survivor with bad knees, all because of Karen Traviss's desire to keep Fett and the Mandalorians relevant. Not to mention the 12+ books where she hung around uselessly before even getting to that point. Twelve books where her twin brother received an obscene amount of god-modding.
Kahlan in Terry Goodkind's The Sword of Truth series and even more so in Legend of the Seeker. Also Cara, and by extension the rest of the Mord-Sith. In the books series, Nicci later becomes this as well.
In the Temeraire series, there are female captains of dragons — and they are almost exclusively captains of the light-heavyweight acid-spitting Longwing breed, critical to Britain's combat formations. There are even three variants presented; a more matronly, heavyset, ladylike woman, a shy young woman who in any other service would be the Sweet Polly Oliver, and the middle road of a woman approaching early middle age with a daughter in the service with a mannish stride and a penchant for smoking and drinking.
Margo Smith of Time Scout, once she takes her levels in badass. She can kick your ass unarmed or with a blade of her choice, or put a bullet in your eye with a pistol at fifty feet, or a rifle at fifty yards.
All of Tamora Pierce's Tortall protagonists (with the possible exception of Aly, who's more of a Spy/Trickster, but can still hold her own in a fight).
Daine may be an exception as well; she's more of a certified nature girl who can shoot a bow and use a slingshot, but doesn't have any explicit powers of destruction unless you tell her that you murdered her beloved teacher. Then she gets angry.
Her prowess with a longbow against the Stormwings would certainly qualify her in the first book, though.
Tamora Pierce says outright that she wanted to write stories for children featuring "girls who kick butt."
Tally Youngblood in the third and fourth books of Scott Westerfeld's Uglies series since she's a special. Shay and the rest of the specials/cutters and the Sly Girls form book four also apply for this trope.
Queen Luxa. Pretty much a requirement, with the humans nearly always at war with the rats.
Okay, pretty much all female characters save Nerissa.
Cutlass Cate and, to a lesser extent, Cheng Li, in Vampirates.
Ellie Quinn and Cordelia Naismith Vorkosigan from Lois McMaster Bujold's Vorkosigan Saga, although Cordelia seems to have retired after the events of Barrayar, at least in terms of physical arse-kicking.
As the basic function of everyone in Warrior Cats is to fight or help the fighters, the females of the series are generally treated about the same as males. This means much ass-kicking in battle.
Just about every important female character in The Wheel of Time, though Birgitte is the one that most embodies the trope.
Since combat is never purely in the cockpit, most of the women in the books of the X-Wing Series count. Shalla Nelprin would probably have gotten along well with Plourr, above.
Action Girls were popular in classical literature. Examples include the goddesses Athena (Lady of War) and Artemis, Penthesilea the Amazon Queen who appeared ancient epic cycles (and later Kleist's play) and Camilla in Virgil's The Aeneid. The popularity of Amazon women waned in Middle Ages, but they were to make a comeback in Renaissance epic in the form of female knights such as Bradamante and Marfisa in Ariosto's Orlando Furioso, Clorinda in Tasso's Gerusalemme Liberata, and Belphoebe, Britomart, and Palladine in Spenser's The Faerie Queene. In the latter poem, Spenser laments the scarcity of Action Girls in his own time and bids females to start kicking ass again as they did in the old days (because he knew Queen Elizabeth would appreciate it).
Brandon Sanderson seems to like this trope. The main character of Mistborn: The Original Trilogy is Vin, who is one of the biggest Badasses in a trilogy full of them even before she becomes a god, and in the first book she has a Dark Action Girl nemesis, Lady Shan. Sarene from Elantris is more of a political Chessmaster type, but she fences in her spare time and is good enough to hold her own against the Big Bad, a magically enhanced warrior monk. Warbreaker has no really solid example, though Vivenna seems to be becoming an Action Girl in training by the end. Also, all, or at least most, Parshendi females in The Stormlight Archive, as confirmed by the teaser readings for book 2, in fact the Parshendi Shardbearer Dalinar fought is one.
Novelist Christopher Brookmyre's kung fu cop, Angelique de Xavia. She kills terrorists with her bare hands, and responds to the Big Bad's expository speech by shooting him in the spine and then cutting out his eye to use on a retinal scanner. She's also technically a Violent Glaswegian, especially considering she's a Rangers fan, but since she's about five feet tall and of south Asian ancestry you might not realise it to look at her.
Honor Harrington from David Weber's Honorverse novels not only commands starships (and later in the series, entire fleets), but on occasion takes part in various forms of hand-to-hand combat. She's an all round example of the action woman who's both smart and physically very capable.
And then there's In Fury Born's Alicia Devries. In any other setting, a character who gets into university (the equivalent of Oxford or Cambridge, no less) at the age of fourteen, completes a five-year degree in three and a half, joins the Imperial Marines, graduates in second place from Camp Mackenzie, sets a new small arms record in the process, gets accepted for a Recon tour straght out of said basic training, then earns a Silver Star on that tour (by killingmore than fifty GLF separatists) would count as a Mary Sue. In this case, it "merely" makes her a promising recruit for an entire organisation of people who are just as good if not better. And that describes the events of the first third of the book.
Safehold has Sharleyan, who provides cover fire for her bodyguards during an attempt on her life, and is noted to be a better shot then some of them, and in another instances after being shot, and breaking three ribs despite high-tech protective fabric, continues on with what she was doing for the rest of the day. Also the main protagonist might technically count, since he's the cybernetic avatar of a woman.
SF writer James H Schmitz was a big fan of this trope before it became popular. Most of his female protagonists (which is most of his protagonists) fit the mold:
Éowyn, of course, from The Lord of the Rings. A Lady of War who pulls a Sweet Polly Oliver and kills the leader of the Ringwraiths. Tolkien had actually initially planned to have her die in that battle, but his wife liked her so much that he had her survive to marry Faramir—who was his Author Avatar. Women of Rohan in general are described as essentially an entire race of Action Girls.
Galadriel came to Middle-earth out of the West precisely because she desired power and a realm of her own, and she got it. And don't forget that during the events of The Lord of the Rings Galadriel personallythrew down the fortress of Dol Guldur.
Lúthien Tinúviel pulled off quite a bit of Bad Assery during the Quest for the Silmaril. Not content to wait behind while Beren did all the heroing, after escaping a prison her father confined her to precisely to keep her from following him, she went alone to Tol-in-Gaurhoth, stronghold of Sauron, to rescue Beren with only the hound Húan to aid her, and afterwards journeyed with him into Angband itself and stood before Morgoth, enchanting him into sleep with her singing and dancing. It should be remembered that music has great power in Middle-earth.
Haleth, daughter of Haldad, was elected Chieftain of the Second House of the Edain because she had valor to match the men, and led to this people being known as the House of Haleth.
Any heroine from a J.T. Edson novel. Calamity Jane got her series.
Mercedes Lackey examples: Georgina (One Good Knight), Tarma (Oathbound series), Elspeth (Mage Winds trilogy) Kerowyn (By the Sword, appearances in Mage Winds and Mage Storms), Silverblade (Silver Gryphon, though she's a bit iffy).
Robert E. Howard wrote some surprisingly strong female characters considering his time, genre and upbringing, including Valeria, Dark Agnes, Tarala, Helen Tavrel, Conchita and the original Red Sonya (totally different and far more realistic than the character better known from Marvel comics and the movie).
And don't forget Tiffany Aching, who overpowered the Queen of the Elves with only a frying pan on her home turf, and to whom Mistress Weatherwax took off her hat in respect, at the age of nine. That's just the start of her adventures.
Even Sybil has her moments. On two occasions, in Night Watch and Guards! Guards!, she responds to trespassers by getting down one of the ornamental swords from the wall. She even stops murderous dwarfs with a song from an opera in The Fifth Elephant.
Don't forget Adora Belle Dearheart (do NOT comment on the name) from Going Postal. She chain smokes and threatens to put the heel of her stiletto through a man's foot, is a trained ballerina and can kick like a mule.
And then there are the Good Omens ones conceived with Neil Gaiman. War is the quintessential Amazon, and then there's of course Pepper. Arguments could be made for putting Anathema and Agnes Nutter into this category as well; they were certainly badass enough in their own ways.
And let's not forget Conina, Cohen the Barbarian's daughter. She laments that she's quite literally an action girl to the core - she wants to be a hairdresser, but get anything that can be used even vaguely as a weapon in her hands...(even without one, she's not someone you want to mess with.)
Nerve Zero features an entire monastic order of Action Girls: the Sekhinim.
The imaginary prehistoric Britain of When Women Were Warriors contains, as the title indicates, a plethora of women warriors (including generals); the main character is a warrior-in-training.
Chronicles Of Magic has quite a few of these, the two most prominent being Anri Adachi (a spy and assassin) and Skeeter Traps (a ten year-old girl trained to kill grown men).