Tywin shouldn’t be on that list at all. He’s amoral, but far from evil or a monster. The second-to-worst thing you could say about the guy is that he betrayed a king that was murdering people at random, and the worst thing you can say about him is that he took his time doing so.
Biter and Rorge are both psychopath criminals. I guess they are by definition monsters, but they’re not really sane. Gregor Clegane and Vargo Hoat I’ll give you, along with most of Clegane’s warband and the larger part of the Bloody Mummers. I seem to recall that the books try to humanize a couple of them a little bit by suggesting that many of them started out as decent, upstanding people who were slowly worn down into their monstrous selves by years of raiding.
Craster is scum who left society to live by his own rules (which are terrible), and there is very little defense for his sacrifice of male babies… but at least you can see the reasons for his monstrous actions; he doesn’t seem to take much pleasure in them.
Joffrey is the most interesting though. Yes he’s a bastard of the highest order, but Martin (in both the books and the show) goes out of his way to show that much of his shitty nature was the result of a toxic mixture of unlimited wealth, privilege, a helicopter mother mother who would not ever permit him to be disciplined, and two fathers who (for different reasons) could not break through Cersai’s protective cordon and raise him properly. So yes, he’s monstrous, but Martin’s point is that Joffrey is less an outside antagonist than a symbol of the failure of some of the other characters.
This is driven home later…
In a scene not show in the TV show yet
… when Tyrion is looking down at a slowly-choking Joffrey and realizes that no matter how much hatred the kid engendered in him moments before, he is at his core just a 14-year-old boy who had all sorts of time to become something greater than he was then… especially given good guidance and advice.
But again: Martin’s point. Both Ned and Brienne must temper their “white hat” ways and see the shades of gray in order to survive. Some succeed better than others, obviously.
Mormont is a good example of a guy who succeeds by living in the gray area. He is kind and chooses to do good things, but he also ignores (and thus tacitly endorses) Craster’s actions. He insists on the Black Watch keeping to their oaths… except he really doesn’t.
Sam I’ll give you. Bran too, I guess – he’s kind of the anti-Joffrey; someone raised well who is forced to come to a strength of character due to hardship.
The Reed kids are such cyphers it’s tough to tell what’s up with them.