User is Rule of Cool personified, being able to perform outright insane stunts that would be very difficult to pull off, or would get a normal person trying them killed several times over, while looking cool doing it. Note: There is a difference between being a badass and being quite powerful and/or lucky, though some may be a little of both.
Duke Nukem (Duke Nukem franchise) kicks alien ass and looks good doing it.
Vegeta (Dragon Ball franchise) has pulled of badass feats such as holding his own as a Super Saiyan 2 against Kid Buu, a monster that defeated a Super Saiyan 3 without seeming to suffer any fatigue, and even made Buu back up in fear of his resilience and determination.
Various human characters such as Leon Scott Kennedy (Resident Evil franchise) are able to perform difficult acrobatic feats and survive insurmountable damage that would be fatal to normal people.
The MacManus brothers, Connor and Murphy (Boondock Saints films) are able to simultaneously fire two Desert Eagles without recoil, seem to have unlimited ammo and survive against all odds by pulling off seemingly impossible feats that border on dumb luck.
Barney Stinson (How I Met Your Mother) has gone past what is possible, to the place where the possible and the impossible meet to become... the possimpible.
Feedback (Ben 10 Omniverse) is considered as Ben's favorite alien and has defeated most of Ben's foes and has more wins than loses.
Juvie (Valkyrie Crusade) is a badass.
Zohan (You Don't Mess with the Zohan) uses his power in the most badass ways, such as folding his enemy to pretzel or putting piranha in his swimsuit.
Like most Abnormals, Medaka Kurokami (Medaka Box) can achieve incredible feats, such as catching cascade of bullets with her mouth.
Not only can Weird-Ass Guitar Guy (Channel Awesome) play a multi-necked electric guitar that can shoot dinosaur missels, but he wears a blindfold because his body is full of so much testosterone that his eyes literally shoot shark-shaped explosions.
Germany (Axis Powers Hetalia) can break a spoon with his bare hands, along with other things.
Jotaro Kujo (Jojo's Bizarre Adventure)
Mr.Smith (Shoot' Em Up)
There's a reason why he's called Invincible (Image Comics).