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.
A character who either does the right thing for the wrong reason or the wrong things for the right reasons as a kind of twisted version of a hero. Really any hero type character that doesn’t do the right things for the right reasons.
Punisher is an anti-hero because he takes things way too far.
Han Solo is an anti-hero because he is a scoundrel who happened to do the right thing a few times.
“The right thing” is also in the eye of the beholder. The killing of that healthcare CEO for example.
You’re right. I saw a mass murderer stopped for good.