Zur-En-Arrh is a back up personality of Batman as seen in the comic Batman R.I.P. He makes a few appearances in the Lapisverse.
In the past, the psychiatrist Simon Hurt was hired by Batman to oversee an isolation experiment. During this process, he gave Bruce Wayne a post-hypnotic trigger connected to the phrase "Zur-En-Arrh", young Bruce Wayne's mishearing of his father's last words ("the sad thing is they'd probably throw someone like Zorro in Arkham"). Many years later, Doctor Hurt was working with the Black Glove when they decided to target Batman and his allies, first spreading information to the effect that Batman's father somehow survived his murder by Joe Chill. Then, using the Zur-En-Arrh trigger, in conjunction with drugs, he sent a dazed and confused Bruce Wayne onto the streets of Gotham with no memory of his life.
In World War X, Zur-En-Arrh Batman is one of the starting characters. He is far more violent than the normal Batman and has increased speed and strength (mainly because he thought he really was more powerful than he actually was). While he lacks Batman’s prep-time ability, he can be guided by Bat-Mite, who helps him make choices. Whether these choices are right or not are unclear.
Zur-En-Arrh Batman also appears as a secret character in Fighters of Lapis 5, where his unlock conditions is to clear Classic with Batman on European Impossible.