he knows it's wrong but he's overcome with so much grief, suffering and hatred that he just doesn't care anymore or he wants vengeance on the rest of the world.
Depends on the character.
ONE type of "evil character" could be so as you described.
But this is not the only type.
Just believe, for example, someone who is a racist. He believes it is "good" to perform a genocide. It's what he (or she) believes in, there is no "he knows it's wrong", because there simply is no "wrong" in his or her belief-system.
Fanatics act the same.
There are other types of "evil characters", I suppose, which differ only in som,e points - minor points rto our eyes, maybe, but possibly fundamental in this character's layout.
