In the fanfic Macushla, Stephanie Brown becomes one: after her father is killed for unknown reasons by the league of shadows, she's taken to serve under Talia al Ghul. She's a master assassin before she's 18 years old and becomes Damian Wayne's bodyguard/Morality Pet. (After Talia fakes Stephanie's death and sends her away because she and Damian were too close, he leaves the League and asks to join Dick Grayson of his own will).
Remember how Yuuno was in Lyrical Nanoha? In Blood That Flows, he's easily as badass as any of the main characters and can hold his own against Gods and Demons just as well as any of the other characters in the story.
In the stories written by Crossoverpairinglover on Fanfiction.net, virtually every character gets upgraded to a point they are badasses. Genuine Lockharts, super saiyan-like Sakuras, Apollos who create black holes, etc.
In Unfamiliar, almost every canon character from Zero no Tsukaima (but especially Princess Henrietta) gets a massive competence boost and a power upgrade. Considering that they're expected to cope with AlexMercer, this is perfectly understandable.
Many canon characters from YuYuGiDigiMoon have given power ups: such as the Digimon Tamers receiving beast powers base on the Four Chinese Symbols, and the Sailor Senshi receiving the mysterious Valkyrie forms.
Justice League of Equestria: Deathstroke has always been a skilled fighter in The DCU, but here he manages to get the drop on Rainbow Dash (this universe's equivalent to Superman) in their first encounter, and then manages to almost defeat her again during their fight in Cloudsdale.
SeverusSnape has been spiking Lord Voldemort's father's grave with every dangerous drug and poison known to wizardkind (and LSD—because it might affect him), as well as every other grave in the cemetery on account of Voldemort might have moved the gravestone, and the graves of every other ancestor of Voldemort's that he and Dumbledore could track down, just in case. Too badVoldemort foresaw this contingency and, since he couldn't move his father's bones if he wants the resurrection spell to work, moved the entire rest of the cemetery to an entirely different location and memory-charmed the local Muggles.
Harry Potter, in so many ways. Here's his following plan:
Quirrell in canon is a simpering stutterer who's a host to Voldemort. Word of God says this Quirrell is possessed by Voldemort, which now makes him the following: Evil Mentor to Harry, a sixth-dan in an unspecified martial art, and he horcruxed the pioneer probe! Oh, and then he went and tricked Harry into breaking Bellatrix Lestrange out of Azkaban.
Blaise Zabini went from Draco's crony to a quintupple agent in a war with only three sides.
In Horseshoes and Hand Grenades, nearly every single character who ever appeared in Kamen Rider Fourze have gone into fighting mode. This ranges from Yuki Jojima using her Hayabusa Plushie as a boxing glove, Chuta Ohsugi fighting off his former love interest, Sarina Sonada and minor characters like the ones in the Amanogawa High Glee Club consist of a sword wielder, a samurai and a ninja.
Contract Labor: In direct contrast to the Extreme Doormat he was in canon, Keitaro actually has some backbone and is far more willing to stand up to and for the Hinata's residents, even managing to defeat Motoko in an honor duel.
Aleph: Nanoha showed us that the Monsters of the Week could be a backdrop to the real meat of the plot, the character interaction, but then Madoka came along and showed us that the Monsters can still be legitimately, vividly scary. And Game Theory is very much a post-Madoka story, with the harsher rules and the scarier monsters and so on.
Also, pretty much all the characters over the age of about sixteen or so get a significant competence boost. Notably, they aren't any more powerful, but they use what they have much more effectively because they employ proper tactics. Especially Precia.
The Wolkenritter in particular have received a major upgrade in skill. They aren't any more powerful, but they show the experience and tactical acumen that would be expected of centuries old combat constructs.
Yukino in Perfection Is Overrated. In the original series, her Child was only good for surveillance, and left her easily defeated by Shizuru. In this fic, she realizes that while she's not the best in a straight-up fight, she can use her powers to tip the balance of power in her favor at crucial moments, such as when she incapacitates Shiho, enabling Mai to win her battle without Yuuichi dying, and when she, in the final battle, uses her Child's abilities to immobilize one of the last remaining SUEs' Child long enough for Natsuki to finish her off.
This trope is a staple for the villains of Ultimate Sleepwalker: The New Dreams and Ultimate Spider Woman: Change With The Light. Characters like 8-Ball, the Brothers Grimm, the Chain Gang and Jack O'Lantern were all C-lister villains, at best, in the original comics. In the Earth-2706 verse, though, they're exceptionally deadly threats, forming the focus of the Fics.
Mimic is said by Princess Luna to have been the first, and only, mortal pony to injure Discord, by kicking him in the face at supersonic speeds until she knocked his tooth out. He killed her afterwards, but still. Starsong probably also counts, managing to fend off Discord's brother Anarchy for a considerable time.
While Princess Cadence turned out to be pretty badass in canon, the version of her in this series was able to take on an avatar of Discord's father Havoc and not only survive, but it's implied that she won.
Rainbooms and Royalty has Zecora, while still being The Obi-Wan to the Mane Six like in canon, also proved personally fantastic repeatedly over the course of the series, with such highlights as saving Rainbow Dash from the Shadowbolts, fighting Nightmare Moon one-on-one, and saving Dinky, Pipsqueak, and Alula from King Sombra's bushwoolie Mooks.
Xenophilia turns Lyra Heartstrings into a grandmaster of the Still Way, the only Unicorn-exclusive martial art. She's described by Rainbow Dash as "probably one of the five or six most dangerous ponies in Equestria, even counting the Princesses," and the only pony in town other than Twilight who could beat her in a serious fight. Chapter 9 reveals her to be an auxiliary Royal Guard, and we also see her in action.
Lero: Wow. I had no idea. She's always been really friendly to me.
Rainbow Dash: (giggling) Yeah, I’ve heard that about her. Total sweetheart, you’d never guess that she could kill you in half a second from, like, three hundred bodylengths away.
In many Naruto fanfics, the title character and his Academy teacher, Umino Iruka, tend to get an odd power-up. In the manga, Naruto is painting on the monument in front of an assembled crowd of ninjas until Iruka calls him down. In the anime, Naruto manages to dodge two low-ranked Chunin in the first episode before his teacher appears behind him once he assumes the coast is clear. However, in fanfics, he tends to outrun and outmaneuver Chunin, Jonin, Anbu and even occasionally the Hokage, for hours, with Iruka being the only person able to catch him, usually within ten minutes of setting out. How Iruka catches the boy who makes Houdini look like an amateur is rarely explained. In certain fanfics, the author explicitly labels Naruto in the description as "Smart", "Strong" and/or "Godlike.
RWBY Reckoning takes the normally bumbling Jaune Arc, a guy who is nothing like his legendary ancestors, and makes him able to build a functioning time bomb with approximately 18 flares, some duct tape, and some scraps. And it's powerful enough to shred the stomach of a very large Grimm.
Clash of the Elements: Cackletta wasn't really much of a threat in Mario & Luigi: Superstar Saga, being an unimpressive mage with an easy boss fight halfway through her game. In this story, on the other hand, she's a Manipulative Bastard of the highest degree, a two-thousand year old remnant of the Dark King's forces who caused the legend of the Shadow Queen just to extend her own life and she has also become a Chessmaster who successfully managed to outwit Big Goods, such as Alpha, the Star Spirits, and an omniscient trio of beings known as "the higher-ups". Implications exist to suggest she has also been able to control the Heartless.
Rumia is lowest of the low in Gensokyo's hierarchy, weak and with a useless power. It's widely speculated however that she possesses a Superpowered Evil Side, meaning most fan works featuring her give her an appropriate power boost, though the degree of the boost varies vastly.
Touhou Nekokayou subverts this trope, making her slightly more powerful, but still comic relief.
Imperfect Metamorphosis's take on Kotohime, who was a generally ineffectual and totally delusional combatant in her original appearance. In this Fic, she's graduated to the rank of Beleaguered Assistant to Yukari herself, running Gensokyo's first police force, and at one poit, she delivers a beatdown to Marisa Kirisame for disintegrating one of her officers (she got better).
Mokou is already an immortal powerhouse and EX-Boss. Touhou Ibunshu has her possess the powers of a Physical God, giving her the strength to go toe-to-toe with Yukari after creating an army of thousands of kashoyo.
In Worldwar: War of Equals, all of South America, Central America, and Eastern Europe put up much more of a fight than they did in the source material. Human tanks qualify as well. In the original novels, even the best Human tanks of the 1940s could easily be destroyed by a single Landcruiser. Thanks to tank technology advancing in the last couple of decades, our tanks are either equal to or superior to their Landcruisers.