Blazer from the World of Warcraft epic "Tales of the Past III" goes from a cocky rogue who couldn't defeat a horde of undead, to a Badass Fist-Of-An-Angry-God paladin who wields a ancient weapon after spending time training in the emerald dream with death knight Mograine (whose control under the Kel'Thurzad had been broken). Notable in the beginning of the fight with Arthas http://www.youtube.com/watch?v=HBMfumHrDRE&feature=related
Tucker, the lazy pimp wannabe from Red vs. Blue suddenly becomes effective once he gets his energy sword. He takes another level when Wyoming locks the whole canyon into a time loop. Tucker is left immune to its amnesia-inducing effects (due to the sword), allowing him to act with advance knowledge of the situation.
Church: Hey you know what, I kinda like this new all-knowing badass Tucker. He's certainly a lot better than the old one.
Similarly, in the climax of Red vs. Blue: Reconstruction, Church embraces his AI heritage and stops The Meta by entering its collective mind. Previously, he was unable to even hit a target at point-blank range.
In Recreation, Tucker returns and shows off his mad skills by taking on the entire digging team, seemingly by himself.
In Revelation, Grif and Sarge come to Simmons and Doc's rescue, but are confronted by Washington. After a couple of failed cues, Grif bursts through a wall with the warthog after Washington has disarmed Sarge. Grif hits Washington, and after a brief drive around Valhalla flings Washington off of the Warthog. As Washington cocks Sarge's shotgun in midair, Sarge timely shows up and takes the shotgun right out of his hands, jumps in the Warthog with Grif, and shoots the fusion coils that Washington landed by. Take into account that Washington is just short of a One-Man Army, and it's all the more impressive. What's more, not only do they beat Washington, but they do it with style.
However, Sarge did mess up his one-liner, so points off for that.
In the same season, as difficult as it may be to believe already high-level badass Tex has apparently taken another level in badass. Meta also spent a lot of that season as an Iron Buttmonkey, but redeemed himself in the fight with Tex and won, no less.
Honestly, with the entire season but this episode in particular, the show itself Took a Level in Badass.
Emma in lonelygirl15 appears to have done this in between "I Love You All" and "Operation Emma", largely as a result of having to fend for herself and witnessing Elizabeth's murder.
Dave (or Dawei) of Pure Pwnage was a quiet, withdrawn sort of guy at first. He absolutely refused to play any video games until a furious micro (a combat skill based on game-playing ability) battle threatened the lives of his friends. After a flashback showing a tragic gaming incident that killed/injured his sisters, he finally snaps and proves to be an incredible user of micro, effectively taking a level in badass and reverting to the arrogant, snarky personality he had in his past.
Ahatake Kurosaki from a Bleach fanfiction might qualify. In a previous arc, the then-current villain, effortlessly split his Bankai in half. Later, Ahatake was kidnapped (for training purposes) by Kisuke, and when he came back on the scene to challenge Takahashi, he surprised him with a backhand slap to the face, and in the fight, equaled him in speed and strength, and taunted him.
Unfortunately, it didn't last due to the slip-up he made, but it was good while it lasted.
Once she got behind the controls of the helicopter Pegs from We're Alive gained quite a bit of confidence, even telling both Datu and Michael to shut up during chapter 24.
Edward Borman takes... well, maybe half a level in The Mercury Men. While he doesn't quite reach the level of badass and is still cowardly, his marksmanship (once he remembers to keep his eyes open!), willingness to put himself into harms way and his ability to think on his feet do improve considerably over the course of the first nine episodes, especially after his talk with Dr. Tomorrow.
Taylor, the protagonist of Worm, does this over the course of the story, going from a victim of severe high school bullying to a member of a formidable team of superpowered teenage villains, and also manages to take down a few powerful villains and heroes on her own as well.
Theo Anders goes from a wimpy, overweight teenager to the hero Golem, capable of taking on multiple members of the Slaughterhouse Nine and winning.
Stealth from The Quest served as one of Diesel's henchmen in Season One, and didn't really have all that much special about him. During his appearance in Season Two, he's learned to turn invisible, runs rings around Crimson and his friends, and requires two superheroes to take down.
Most of the reviews for That Guy with the Glasses get this, especially in the anniversary events, which become increasingly more dangerous and which they still manage to handle.