I tend to think of sports games when it comes to Big Head Mode, but Rocksteady Studios was willing to apply the equally creepy and funny style to Batman: Arkham City. Good on you!
All that’s required to enable the mode is holding down both triggers and moving the analog sticks in a circular fashion. Though the video demonstration showed this happening while the Cryptographic Sequencer was out, I don’t think that having the device active is a requirement.
Haven’t had time to try this out for myself, but others are saying you can even initiate it from the main menu. One has to wonder what else Rocksteady has hidden in Arkham City.