There is only one way in

Save the damsel, but is she in distress?

Become the Bat

Complete story mode on Easy difficulty

Defeat the giant Titan Ivy plant

Venture into Killer Croc's lair and come out alive

Complete one combat challenge without taking damage

Defeat two Titan Henchmen at once

String up one henchman and drop him to surprise a second (any play mode)

Solve 25% of Riddler challenges

Face your biggest fears and keep your sanity

Gain access to Arkham Mansion after it is locked down by the Joker