Penguin and Joker

Penguin is a perfect foil to Batman. While Batman uses his wealth to provide himself with technology to discombobulate his opponents, the Penguin has enough money to compete. Unlike other Batman villains, he isn't mentally disturbed, making his actions cold and calculated. 

Speaking of disturbed, the Joker is Batman's archnemesis. Batman wants order, the Joker wants chaos. The Joker doesn't want vengeance or money, he just wants to watch the world burn. How do you fight an enemy with such insane motivations? It's a tough job, but Batman's gotta do it.