There are no wrong answers, only your opinions 🙂
Personally, I think an anti-hero is a bad guy that does good things. He might cheat on his wife, steal, gamble, etc, but when it “matters,” he ends up on the side of what’s good.
Han Solo is an example that comes to mind.
John Constantine is a good example. He will do the right thing, even if it means sacrificing one of his oldest friends to eternal damnation to do it.
And his past is littered with people he’s done that to. It’s not a one off “Oh, sorry mate, only way to get this done is to… you know, infest you with a swarm of demon bugs…”