We've given a breakdown of Harley Quinn so of course we're gonna drop an honourable mention to the Joker.
The Archenemy of Batman, Harley Quinns estranged lover, potential fashion icon- the Joker does it all. The Joker incorporates a punk style with his purple suits and neon green quiff- a fuck you to society incorporated through his style and the fear he instills in the public. Popular tattoos of the Joker always show off his maniacal chelsea-smile grin and smeared dark eye makeup.
If you're not feeling to go for hyper-realism with Joker tattoos, why not use some of the DC comics he is frequently published in for inspiration. Think comic book illustrations of the Joker with bright explosions and holding a pack of cards. Think the Casino, gun slingin side to the Joker. These tattoos will help provide a sick starting point.