I wanted to post this because Anti-Hero has been done but Anti-Villain hasn't and I think it's just as important. For how to write the character see how to write an Anti-Hero.
1. They're not evil.
Wait? Did you just say their not evil? Yes. There is a difference. Evil: Thanos. Not evil: Loki. There is a difference between these characters. The best I've ever heard it said was: "Theirs two kinds of evil. Theirs the people that choose to be evil and the people that are forced to be." Thanos is evil. He's aware that he's evil. He chooses to be evil. He wants to be evil. Loki isn't evil. A villain? For sure. But evil? No! If you've read recent Journey into Mystery you'll find he fears being evil. Evil: Joker. Not evil: Deathstroke. Joker is pure evil. He's insane. He LIKES being evil. Deathstroke was forced to be evil.
2. They're not an Anti-Hero
Anti-Hero: Hulk. Hulk is an Anti-Hero. He's not an Anti-Villain. Theirs a difference. Anti-Hero: Punisher. Who is Punisher fighting? Bad guys. I said Deathstroke and Loki were Anti-Villains. Who do they fight? Heroes. So Anti-Villains fight heroes? But there not evil? Will I retract my former statement: They are evil. Yet their not. See! This is a very important thing. And IT HASN'T BEEN POSTED! The general idea of writing a not evil, evil person is very hard.
3. They are evil.
Before you think I'm insane, let me explain: Their not evil and that's final. But they're a villain, that's final. Their not an Anti-Hero and that's final. And their evil that's final. And for sure their not good. Wait! Their not good. So is Deadpool evil? Is Red Hulk evil? No. But if there not good then they have to be evil. Or are they traveling the fine line? The answer is.... NO. Their is no fine line. You're either evil or your good. So what are they? Their evil. So then, I ask you again is Deadpool evil? Is Red Hulk evil? No their not. There not evil. Are they good? Yes. Are they Anti-Heroes? No. So their good Anti-Villains? Wait. This makes no sense. Read on.
4. Are they good?
So, are they good? Well their not evil. Or are they? Is Hulk good? Is Punisher good? Yes. Or I ask you again. Are they? Are they evil? They've killed plenty innocent people. Does that make them villians? Now I ask you when is the last time you've seen Deadpool kill an innocent citizen that he wasn't hired to? When have you seen Red Hulk kill innocent people? Exactly. So are they good? You tell me