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.
By the time of Season 12, the crew are overall much more competent than before, though they still fail irregularly.
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.
In the Volume 1 finale of RWBY, Blake Belladonna struggles to hold her own against Roman Torchwick, even with help, and the fight had to be interrupted. In the Volume 2 finale, she has a second battle with him, with no assistance this time. Guess who wins? Hint: Not Roman.
The titular heroes of X-Ray and Vav first start out as a pair of Super Zeroes who couldn't stop a pair of crooks without turning the city into a crater. Episode 4, the finally get their heads on straight and rescue the entire city from the clutches of the Corpirate.
In the fourth novel and Season 5 Arthéon became this by getting promoted from mere Player Character to a player-controlled world boss whose stats are superior to all three Ultimate Gamer 386 characters of the franchise taken together.
The duel between Omega Zell and Gaea shown in the webseries was preceded by showing that the trope applies to both parties: Gaea broke out of the "coward" part of her usually Dirty Coward self merely by asking for the duel and keeping up with Omega Zell who's starting to reap the benefits of being in Justice guild.
The various members of the Yogscast have had numerous failings in their Minecraft series, but have improved immensely given time:
Kim Richards started as the Naïve Newcomer when it came to Minecraft, but eventually learned to improve. She was the first player on the company server to successfully land the rocket without dying (everyone else who had attempted this had died somehow). When left to run Panda Labs on her own, she manages to kill all of Hat Films by herself.
Simon Lane's building skills were initially somewhat dire, but by Moonquest he builds a fairly cool airship which proves handy for the crew. Come Hole Diggers and he ends up designing a space station... which can mine from other dimensions.