[Nogrod]

Violent (furious, vicious, destructive)

Battles are violent by definition, so a battle offered here as an example of violence should have more to offer than the Battle of Bywater - unless you took the sarcastic mode. But also more than the Battle of the Pelennor Fields. Like everything else also battles waned as the ages piled up and the main battle of the third age is more or less but child's play compared to those of the second or first age: think of the Valar and Maiar clashing in the first wars - or all the great Noldorin heroes clashing with Balrogs and other Maiar creatures - and the numbers of elves, men, dwarves, orcs, creatures of any kind going down in those battles. Compared with those the Battle of the Pelennor Fields is child's row at the sandbox.

I would discard the battles then.

I would also discard Menegroth and the plains of Gorgoroth as they were just places and places are not violent but creatures doing things in those places.

What tp said about Tar Atanamir is to the point. But with Ar Pharazôn I'd have to disagree with him and remind you that he wasn't that violent as a person. You could say he was lots of bad stuff, also vicious and destructive, but one should fill the main adjective (violent) first and then get support from the other ones - if the judge is willing to consider them. So I'd discard the Númenorians as well.

That would leave me four choices to whom violence would fit.

Ungoliant
Tulkas
Eol
Beorn

So how about the other / supporting / explanatory / widening adjectives?

Eöl could be said to be vicious in a way and maybe furious, and destructive... well, maybe. But it is clear he has those qualities on a lesser level compared to the other candidates.

Tulkas and Beorn are furious and destructive but not so much vicious. But what they lack in viciousness they gain monumentally by their erraticness or unpredictableness. Both seemed to have this berserk-rage when they didn't quite control themselves - remember Gandalf telling Bilbo & the dwarves not to go out when Beorn was there in a Bear-form but on their peril.

Ungoliant, not surprisingly, seems to fit all the adjectives. Her fury was such that she even challenged Melkor himself, her destructiviness such that she drained all the light from the world - and vicious enough to spawn a whole race of spiders in her bitter hatred against not only the goodies but baddies as well...

Although if one just stresses "violence" I'd pick Tulkas or Beorn. But Ungoliant looks like the perfect pick otherwise.