Maybe he's just a vigilante who got inspired by Batman and so he was similar to him under a different name in another city or country but feels he has surpassed his idol cause Batman will not kill and so that makes him weak,He came to Gotham and used the name Arkham Knight cause of the situation at AA&AC,He wants to kill Batman cause he feels he can be Gotham's future and other villains are just accidentally in the middle of it?
That'd be an interesting new character,There's been others like him in the comics but don't mean he can't be the next new similar guy