Main page: Dead Rising.
How to unlock: Kill at least 10 psychopaths.
Most will be encountered through the campaign's general progression, but the following survivor missions are where others can be found: Mark of the Sniper, Above the Law, A Strange Group, Long Haired Punk, Out of Control, and Photographer's Pride.
The best weapon to use against a psychopath is the Shotgun. One can be found at the very beginning of the game next to one of the survivor's corpses when zombies get inside the mall, and many can be found in the gunshop, which will ironically enough have a psychopath in it that you must defeat before being allowed access.