Let us first define an anti-hero. It is NOT a villain protagonist where the main character(s) or any character we journey through is a full-on hardened criminal or down right evil.
A few examples of villain protagonists I can come up with on the top of my head are Michael Corleone (from the Godfather franchise), Tony Soprano (from The Sopranos), or Walter White (from Breaking Bad). These are not anti-heroes. They are full-on villains who we journey through as protagonists, committing crimes and out right evil for their own abition whether it is good or bad. Walter White might be more of an anti-villain than an anti-hero. But are villains at the end of the day.
Anti-Heroes are ultimate heroes at the end of the day, but lack conventional heroic attributes that make us see them as overwhelmingly flawed individuals.
Examples: Vegeta (from the Dragon Ball franchise). Started out a villian, but evolved into an anti-hero through fighting the same enemies as the heroes. There are times where he was a hero, but mainly he fights his enemies out of his Saiyan pride and his desire to become the strongest. He does however get stronger nowadays to make sure he can fight off Frieza from invading earth, though. Another heroic attribute, sure. But he is arrogant, stubborn, and has an ego. So much so that his latest form is... well Ultra Ego. His arrogance and stubborness is way more exposed in that form.
Another Example is The Punisher from Marvel Comics and Red Hood from DC Comics. Both are heroic in many ways who fight off villains for the greater good, but are ultimately brutal, ruthless, merciless, and flat out psychotic at times when it comes to their methods of killing said villains. Sure, they do fight evil people for the greater good. But their methods can make us question their heroism at many points and time.
So yeah, that's what anti-heroes are. They do heroic things because of their own self-interests, or because it's right despite being vastly brutal.
Now that we have that distinguished, post your Anti-Hero story here. I have mine right out here for you