Anime

Just to be clear, we are talking about villains? (i.e. they don't have to be the antagonist)

In that case:

Saga of Tanya the Evil has got Tanya, who is not only extremely badass as a villainess, but also serves as the series' protagonist.

Otherwise, my pick goes to Quinella from Sword Art Online: Alicization. She is evil but with cause (whether the cause is good is another debate).

Also,

Honourable mention goes to Askeladd from Vinland Saga. I begrudgingly respect him despite his evil acts.

Also,

Satsuki, and later Ragyo, in Kill la Kill kick ass.

Do Ainz and the floor guardians of Nazarick, from Overlord, count?

Knives from the old Trigun. Horrible and capable. The colony ships, July, Rem's relatives, the flying city, and the goals and actions of the Gung-Ho Guns, especially Legato.

Vicious from Cowboy Bebop. "And you will shed tears of scarlet"

That's such a hard question for me to answer. Are we talking about well written and just an excellent foil for the protag? Then Nox the Xellor from Wakfu. Are we talking about one that steals the show every time they're on screen? Then Char in every show he's been in.

Is Reinhard von Lohengramm from Legend Of The Galactic Heroes a villain or protagonist?

I think he winds up being more of a villain in the end.

How about En, the mushroom wizard from Dorohedoro?

Seemingly almost invincible, but he cares about his minions, until he doesn't.

Gurren Lagann by a country mile. Both of the main antagonists of the show are great

Johan Liebert from Monster.

Pretty complex and well written character.

Shougo Makishima from Psycho Pass

Absolute sociopath who could quote Shakespeare in the same breath as slicing someone's neck

Just one quote from him:

All of Roboworld leadership from Redline definitely qualified as badass. Most everything else in Redline too tbh.

One comes to mind, but it doesn't have an anime in a long time. Kind of. Desty Nova from GUNNM. To explain it would be spoilers, and I don't really remember lol

Would need to reread Gunnm and Last Order again.

This is a hard question, but for a quick answer, One Piece has some really nice badass villains.

Naraku from Inuyasha is definitely the most cruel.

Overlord. Ainz Ooal Gown is undoubtedly the villain.