Evangelion 303: In this doujin Shinji, Asuka, Rei, Kaworu... are all of them Ace Pilots, chosen between the military elite to pilot the most advanced war planes ever created... and they are damned good at it.
Higher Learning: Kaoru returns to his home to find Gendo and an armed squad inside it. Kaji thinks that the poor teacher is going to have an imminent appointment with God… when Kaoru makes Gendo backing down and leaving with one single sentence.
In the Uplifted series, the historical figure of Mad Jack Churchill is one, such as when he ties a Gestapo officer to a truck and uses it as a battering ram. Justified, since he really was like that in Real Life, since he captured 42 Germans with a broadsword and went into battle with a longbow across his back.
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.
Minato from Fairly English Story After being framed for terrorism and escaping the city, when he comes back at 150 Mph in his motorcycle he jump, desmaterialize the motorcycle, run at the police and send 10 police pratrols meters in the air AT THE SAME TIME.
Konoha, one of Sylvia's brothers, from Sylvia The Sylveon. He defies his sadistic trainer, first by running off and evolving into the Pokémon he wants when his trainer had another evolution in mind, then, after a beating-up, destroying his Poké Ball, therefore freeing himself.
Chrono Cross fanfic Fellowship has some examples, but the most prominent examples are Draggy, Starky, Skelly, Yoshino, and especially Guile.
Draggy's tendency to fight with his fangs enables him to catch Guile's rod and throw Skelly across the sky (after evolving) with his teeth.
Starky (especially after evolving) can put up a serious fight with many other characters. Draggy has hard time beating him in a sparring match.
Being a Dem Bones, Skelly is able to reattach his bones to his skeleton if they are separated. He cancels out Guile's Unstoppable Rage with this ability.
Yoshino, despite being just an ordinary thirteen-year-old girl from the real world, doesn't hesitate to bash Genie's head with a stone and shove her away just to show Guile that she tries to atone for her acts: abusing Guile with a Freudian Excuse. This act saves Guile's life and puts hers in danger.
Guile. No matter how bloody his fight has been, he never suffers injuries on his back. It's because he always moves straightforward in a battle and never, ever shows his back to his enemies.
Genie too, although she's one of the bad guys and a one-shot character. She is always calm even when her death is seemingly imminent. An angry foe, more people joining a fight, and an evolving foe can't scare her, and she only replies with a flat 'fine' when she sees them.
She regularly takes a mecha capable of tearing apart universes for joyrides, among other things.
When faced with a Mary Sue, she proceeds to GIGA DRILL BREAK the living daylights out of it without breaking a sweat.
She goes to the Dimension of the Metal Gods themselves to acquire the most powerful guitar in the world, Fuckslayer. Said guitar can't even be played by non-Bad Ass characters, and Blake uses a Core Drill to play it. The result literally shatters the earth around her, and she keeps on playing with naught a care in the world. She does this to win a bet.
In fact, the Reactsverse (both Reactsverse!Earth and Ylisse) counts as a World of Badass. Blake is just the premier example.