Badass/Fan Works

Supetastic 6 Unlimited as a whole in Super Milestone Wars 2
The Tamers Forever Series has several examples but Chaos, Rika, Takato, Takeru, Tatsu and (as it is later revealed) Terriermon are by far the most noticeable examples.
In The Tainted Grimoire, characters are this, be they good or evil, for example Judgemaster Cid Randell, aka the strongest man in Jylland, Illua who showed some of her power in the first chapter and Ensei Rou, who defeated 120 mages, without taking any damage.
Light and Misa in Gods of This New World but especially Misa who gets up and keeps fighting the Big Bad after being stabbed in the chest with a sword. Also L pilots a harrier jet and Sayu fights off Mello when her Gun Fu skills when he tries to kidnap her in an Offscreen Moment of Awesome.
Charles Bhephin's version of Shinji Ikari. Yes, that Shinji Ikari. Don't ask, just read.
- We should pitch Academia Nut's version as well, but stay away from the potentially flammable Open Door even if it does have more badasses to its name.
SamJaz's Minato Arisoto, following the steps of Charles Bhephin. Yes, he became so badass, he practically channeled THE GREAT KAMINA!
Though in Command & Conquer Renegade, captain Nick Parker is a certified One-Man Army, in Tiberium Wars, he gets extra badass points. In one chapter, he brings down a Nod Avatar singlehandedly while flipping it the bird, and then calmly walks away from it after chucking a satchel full of artillery shells at its prone body.
Team 8's version of Naruto (who has taken about as many levels in Badass that the canon version did in a tiny fraction of the time).
Enemy of My Enemy's Rukth 'Kilkar, known to his foes as "The Black Sangheili". Like S&W40K above, both this and the above fic are positively filled with badasses out the wazoo.
In the Pokemon fanfic Project Phoenix The main character Robert's alter-ego, Phoenix, is hugely badass. Mostly captured through this picture^{[dead link]} by the author.
Akira from the Deva Series. How do you show you're a bad motherfucker? Why, by taking on and holding off most of the combat leads simultaneously, that's how.
Kyon from Kyon: Big Damn Hero. Taking down twelve experienced fighters on your own, complete with Dynamic Entry? Check. Fighting off twenty four Yakuza with two others? Check. Badass Longcoat? Check.
BigD1987 gives us 2 stories with multiple badasses. In The Swordsman and The Gunslinger, we have Kyo Sohma of all people turned into a Japanese swordsman in the Wild West and his partner Jimmy Michaels, a Badass Gunslinger in true Western tradition.
- The other story, Power Rangers GPX, is Power Rangers on extra levels of Badass. The Rangers themselves and the villains themselves could be considered badass.
Latias' Journey is filled with badasses.
- Same goes for the Poké Wars series.
All Grey Wardens from Dragon Age: The Crown of Thorns, especially Badass Longcoat elven mage Alim Surana, who kills demons by making Grim Reaper impersonations.
Deadly Mistakes, a fan-made post-by-post role-play, had a character called Kurgan Junior (yes, daughter of that Kurgan) portrayed as such. Well, until she got killed, that is.
- Ellen "Newt" Ripley Junior (yes, daughter of that Ellen Ripley), another character from the above-mentioned role-play, could easily count as one as well.