In "The North Remembers", Sansa Stark pretty much takes a level and then some. She first kills Ser Shadrich with a knife when he attempts to rape her, then manages to enlist both the Brotherhood after convincing them not to kill Sandor, and the Burned Men by willingly getting her hand burnt, to help her overthrow Littlefinger. This finally culminates with them assaulting the Eyrie whilst Sansa is being tried for murdering Sweetrobin Arryn. The end result, Sansa beating Littlefinger at his own game (along with him getting a well-deserved beatdown courtesy of Lady Stoneheart).
In the Chance Encounter series, Paris, Helen and Briseis, the former becoming a skilled archer, the latter two being skilled swordswomen, and Balian takes a subtle one, picking up a bunch of new moves from the Fellowship and moving more smoothly in battle, going from ordinary Badass Normal levels to, while under mind control and what could be considered a Superpowered Evil Side, fighting Legolas to a standstill.
The Naruto/Justice League Crossover Connecting The Dots does this to most of the Konoha 11, but especially to Tenten. You remember Tenten? Trust me. Not this one.
The Simpsons/Futurama crossover Fast Forward has pretty much all the main characters of either show take major levels in badass (with the exception of Leela, given she was pretty badass to begin with), due to Bender gaining a weaponry upgrade and the human characters (and Zoidberg) gaining a Farnsworth-made upgrade: their own customized, stylish, Transformers-style suit of Powered Armour.
In the Magical Girl Lyrical Nanoha and Harry Potter crossover Professor Takamachi, Nanoha manages to do this with a lot of Hogwarts students through a simple means. Physical training to increase physical and magical stamina, math to increase their ability to focus and multitask better, supervise the DA by putting things into practical terms, and then organizing groups to do magical sparring together as teams in simulated combat. This pays off when the Hogwarts students organize and decimate a Death Eater attack on Hogwarts. It is also hinted that Harry and his group put up a much better fight in the Department of Mysteries.
While in The Wizard In The Shadows, Harry has mostly done his levelling offscreen by the time the story starts, it is quite something to contrast the already Bad Ass Boy-Who-Lived to what he is after four years trapped in Middle Earth in the run up to the War of the Ring: an absurdly - by human standards - fast Knife Nut, an extremely powerful wizard who is more than willing to kill and capable of going toe to toe with the Nazgul - he actively hunts them, and The Dreaded for everything evil in Middle Earth for very good reason, whispered of as 'The Black Wizard'. As noted by the author, this is largely justified by the Kill or be Killed nature of late Third Age Middle-Earth.
He takes further levels in Bad Ass, wielding the Sword of Gryffindor in battle, fending off an army of Dementors (admittedly, he was possessed for that part) after singlehandedly holding an Entropy Ward over all of Helm's Deep for over two hours against continuous assaults from the Uruk-Hai, then destroys a fifth of them by taking command of the storm and raining down lightning. And he was only drawing on outside power to a great extent with the Dementor part. He later takes on Wraith Voldemort, who is present as a balance to the Tenth Walker in a swordfight on the back of a fell beast. Among other acts of obscene badassery.
Just about every character in the series: Boromir and Aragorn each singlehandedly take down one of Sauron's uber-trolls without taking a scratch. Ginny unleashes hell on the Morannon in the form of three firestorm tornadoes (with outside assistance). Ron and Hermione develop into capable sword fighters. Emrys goes from Punch Clock VillainMook who, after a Heel-Face Turn (debatable since he wasn't at all personally evil in the first place) becomes a Badass Normal who kills a (distracted) troll solo, and eventually becomes - at the Black Gate - a part Ainur Empowered Badass Normal who swats trolls like flies. By the sequel, it is vaguely hinted that he can fly, or at least defy gravity, and can move in Super Speed.
Keena Soga, of course, in Keena & the Defendants of Constan Magic Academy, who now no longer is forced to stay out of the way in the battle, takes tons of hits, still gets back up and doesn't even need help to defeat her opponents, even if she hurts them in quite brutal ways.
After the events of Omni-Tamer, Takato becomes the strongest Tamer by far. Unfortunately for him, the one person whose respect and praise he truly desires instead becomes aggressive and spiteful to him out of jealousy, forcing Takato to finally snap.
Dragon Age: The Crown of Thorns has given levels in badass to more than just the dwarven noble Wise Prince protagonist, plus some antagonists (the Sloth Demon, Piotin Aeducan, the Fade Beast-it becomes a rock wraith, etc.)
Kallian Tabris, the city elf, also a Lovable Rogue, finds herself forced to drink Avernus' alchemical potion, making her blood poisonous to darkspawn (and she can even read their attack intentions like some sort of battle precognition). Lady of War indeed.
Alim started out as a One-Man Army blood mage but eventually learned shapeshifting and telepathy. He also seems to avoid the Squishy Wizard trope altogether, though mostly through timely applications of forcefields. One can only wonder what will happen if he ever becomes an Arcane Warrior too.
Alistair didn't get many special powers, but Raonar's tutoring did yield a much higher level of self-confidence, actually making him lose a level in suck. A Magic Knight in his own right.
Theron Mahariel and Gwenith Cousland can still qualify as Badass Normal members, but it is unlikely that the story will end without them also getting some sort of powerup. One might say it is required, considering what happened in the latest chapters (The Archdemon became smarter and more self-aware, possibly able and mentally coherent enough to use blood magic).
Even Trian Aeducan seems to have gone through this after his memorable Break the Haughty several months-long period of being presumed dead after having his death faked against his will (and forced into being roomies with Gorim.
Tohru Honda—No, really— TohruHonda gets this treatment in the Western AU fic The Swordsman and the Gunslinger. On the surface, she appears to be a sweet but she can hold her own in a fight. Even a person who knows her very well is amazed that she can handle an enemy.
Dumbledore's Army and the Year of Darkness is all about Neville Longbottom, and the DA, levelling up in Badass to the point where they're able to stand up to, and fight, Death Eaters on a nearly-equal-to-equal basis.
Another example is "In Cold Blood", wherein Harry is asked by Gringotts to work as a freelancer assassinating Death Eaters for them. The goblins have a magical method that allows them to transplant knowledge from prisoners, so that Harry can fight well beyond the level of his targets. The fic is rather vague about how much knowledge of what Harry gains: all it states is that the first donor is a skilled enough torturer to keep a man on the edge of death for six months, and that after Harry gains the torturer's skill a "seemingly endless" number of donors file in after him, with "everything Harry could possibly use" against his victims.
In "Harry gets Motivated", Harry asks Professor Moody to mind control him into relentlessly forcing himself to study to exclusion of everything except whatever Harry has to do to stay mentally and physically healthy, and to protect himself from Voldemort. This fic ends with Harry draining his bank account to further his studies, refilling it by attacking a giant vault in Malfoy Manor with his new skills, and eventually killing Voldemort so as to ensure he can study uninterrupted.
In the Jackie Chan Adventures fic Queen of All Oni, Jade has done this, having gained increased strength in her new Shadowkhan body (and gaining a knowledge of shadow magic)]], and having put her genre savviness to good use against her former loved ones.
Later in the fic she plans to take MORE levels by finding three magic tablets she can use to increase her magical knowledge further.
In Horseshoes and Hand Grenades, most of the minor characters in the show gets the chance to shine. For example, former Zodiarts Motoyama and Norio become Kamen Riders (Den-O: Sword and Den-O: Wing respectively), while Butt Monkey Chuta Ohsugi beocmes a Badass Teacher willing to take down Dustards, his former love interest and the Big Bad with nothing more than sheer guts and determination. Likewise, comic relief characters like Yuki can now punch a Dustards' light out with a "HAYABUSA PUNCH!"
The Immortal Game: Pretty much all of the Mane Six over the course of the story, but the crowner has to go to Fluttershy of all ponies. During the Final Battle, she somehow taps into Terra's old power as "Princess of the Forest", becoming a Physical Goddess with a flowing mane and something akin to the Royal Canterlot Voice who is able to cow the most powerful dragon alive into a Heel-Face Turn and serving as her mount in a Big Damn Heroes moment. Everyone else (both in and out of universe) is shocked at this, and even Rarity admits to being a little frightened of her
In the Pony POV Series, its easier to list the characters who don't do this. By the end of the Princess Gaia Arc, the mane cast and Trixie are tough enough to fight a Mad God head on and hold their own. Derpy Hooves beats down the mooks of the Big Bad to protect her daughter and is an experienced Companion of the Doctor, Shining Armor is a trained military warrior who managed to fight out of a full on military ambush, Princess Cadence took out an Avatar ofHavoc in the back story (though she can't remember) and is willing to put her life on the line to protect Shining, and the CMC managed to build a functioning time machine. Heck, even Celestia and Luna are complete Badasses in this continuity.
The G1 Mane Cast get this as well, the Rainbow of Light having made them The Ageless. What do they do with it? Spend several thousand years kicking the flank of any monster who dares threaten Pony Kind. This includes managing to beat Discord in a straight up fight (though unfortunately, he managed to escape) and beating back Grogar (who in this universe also counts as this trope, being a Dangerously Genre SavvyEvil Overlord who can go toe to toe with Discord) every 500 years. Of note are Mimic, who managed to fight Discord head on and ultimately break his tooth permanently in a Dying Moment of Awesome, and Shady, who was Discord'sDragon and ultimately redeemed herself by holding him in place for the Princesses to beat him.
Some of the G2 Mane cast get this, considering they end up having to survive After the End when a Class 2 apocalypse hits. Sweetheart becomes a nurse who stops a supercharged version of The Black Death and her husband Teddy goes Papa Wolf and protects his family from corporate thugs and mutations spawned by the blast. Patch is the biggest, as she goes on a quest to rebuild the Rainbow of Light, becoming an Action Girl who overthrows a number of ponies abusing the shards' power. She even manages to beat a dragon in a straight up fight and outwit and beat Grogar. Did we mention she has no special powers outside the Shards slowing down her aging?
Minty Pie from Dark World. When we first meet her? A normal everyday Earth Pony (though one who grew up in Discord's Crapsack World). Then she decides to go help the others in the fight with Discord. She falls into an underground cave and being hailed as The Chosen One by a race of winter spirits. By the time we meet her again, she's defeated her own Big Bad and became an experienced warrior with a Cool Sword. By the time she reaches the Final Battle with Nightmare Paradox, she dodges some fireballs with practiced grace, throwing the time travel scroll that Paradox wanted to force Twilight into using into it in the process and manages to hold her own despite being the only Badass Normal in the group.
In Blind, due to one failed recon mission (that was VERY important) Naruto, Gaara, Hinata and Shino take levels during the time skip. Naruto and Gaara had to due to being declared missing nin with kill on site orders in KUMO where they are hunted like dogs EVERYDAY so they had to toughen up or die. Hinata because of throwing herself in training due to heartbreak (Naruto didn't tell her about the mission and ends up as a missing nin so she takes it hard. Doubly so because they are betrothed) to the point where she can take Neji down in a fair fight. Shino because of anger at his friends being traitors (Naruto and Gaara) and one giving in to depression (Hinata).
Future Sakura in Naruto Mysterious Power, who manages to defeat over half of the main cast, went from being nothing but the main antagonist's sex slave to using the powers of eight tailed beasts and a cursed seal, along with sonic screams and various Chidori-Raikiri versions.
Naruto again in Legacy of the Rasengan: Naruto. Due to misunderstanding something Iruka said, (hearing "the 4th Hokage was a great shinobi WHO just so happened to create his own jutsus." as "The 4th was great BECAUSE he created his own jutsus.") Naruto decides to tell the Angst to fuck off and become a badass with his own collection of jutsu. The kicker being all his jutsu are simple and easy to use but WILL reach Gamebreaker status when he gets older. Examples of his jutsu:
Kaze Tate no Jutsu : Creates a tornado around the user that works to deflect things thrown at him. More chakra = Raging Tornado defense. Can also be used for offense (Naruto used it to stop a Gatsuuga).
Kaze Kiwa no Jutsu : Creates a wind sword that Naruto upgrades to be near Rasengan levels. Since it contains nothing but wind and chakra, its tip causes Massive Damage. Naruto used it to cut through Neji's Kaiten.
A very interesting inversion of this trope comes from the Neon Genesis Evangelion fanfic NGE: Nobody Dies. Shinji Ikari is nostranger toTaking LevelsIn Badass, but Nobody Dies Shinji could be more accurately described as having Lost A Level In Suck; thanks to Yui surviving the backstory, Shinji has grown up into a well-adjusted and perfectly normal teenager, with none of the numerous neuroses that plagued him in canon but also none of the unGodly self-confidence or super-powers other fanfics tend to give him when doing this. It makes for a very interesting take on Shinji's character to see him stick up for Asuka and trade verbal jabs with his classmates when he's not smiting Angels with an Eva-scale BFS or a Wave Motion Gun. Then again, when you're the walking embodiment of This Loser Is You, even becoming an Ordinary High School Student is a big step in the right direction.
Shinji & Warhammer40Ktried to invert this trope in a manner similar to Nobody Dies but the author wound up overshooting the target and turned Shinji into a very straight (and very EPIC) example of this trope instead (Case in point, there's nothing ordinary about an Ordinary High School Student with his own gang and the universal respect and adoration of his entire hometown).
The Poké Wars series takes this trope and dials it Up to Eleven. Each and every surviving character becomes a badass fighter.
The Sun Soul takes this idea and turns it Up to Eleven... for Pokemon. No really, the author manages to take something as innocent as Pokemon and upgrade it into a grim, gruesome, and nightmare-inducing retelling, without going overboard on the crazy. Each character is leaps and bounds ahead of their original counterparts in terms of sheer badassery and so far the story has consisted mostly of adventure, mixed with politics and romance, with plenty of action and Anyone Can Die added in.
Ash Ketchum certainly qualifies. Trainer abilities and savant heritage aside, the lad is dangerous with a knife.
In the Portal2 fanfic Blue Sky Wheatley goes from a Lovable Coward who can hardly even walk...to a Lovable Coward who is willing to sacrifice his life to successfully take down GLaDOS, taking his flaw of bad ideas and weaponising it.
Everyone did in Magica Madoka Veneficus Puella. All of the weapons can be spammed without hesitation. All the characters have enhanced strength and reinforced body structures. Oh, and Homura's a potential goddess.
Sailor Moon Millenials gave this treatment to Chibi-Usaof all people by having her come back from the future as a teenager and newly-christened Neo Sailor Moon. While not exactly a Future Badass, she was at least as useful as the other Senshi on a consistent basis.
In White Devil Of The Moon the Sailor Senshi are becoming this due to getting trained by Nanoha. Most relevant? Sailor Mercury kills Zoicite on her own without support. In the most recent chapter, each of the senshi are able to take on superior odds against their opponents with minimal or no support and win.
Fallen King has everyone to some degree, but especially Joey Wheeler, who becomes the hero of the story.
Matthew Streika, once the living embodiment of the Idiot Ball carrying Wide-Eyed Idealist, now has taken some levels in badass. He threw himself in the way of The Brute's attack, got some nifty magic, and kicked a lot of ass. Shuuji followed in Chapter 2, redeeming himself by making a Heel-Face Turn, and then reducing Medrautto a quivering wreck. Even little Alina, who in the first Canon was an annoying Bratty Half-Pint, became so much more Bad Ass as a Biological Superpowered Magical Weapon. Alina's adoptive little sister, Alexandra "Lexie" Ivanov, starts out only able to summon little lizards and heal people...and she is a Shout-Out to Final Fantasy's Summoner Class...wait, what's she summoning now, a bigger lizard? Nope, you're dead, Adrian. What's that sound? Its the world taking a fear shit: She just summoned Dragon Emperor Andreclav