Armored Batsuit:
To unlock the Armored Batsuit in Challenge mode, complete the game.

Unlockable Challenges:
Unlock the following challenges in story mode by finding the corresponding riddler trophies:

CHALLENGE: HOW TO UNLOCK
Shock and Awe - Find the Riddler Trophy for Botanical Gardens Riddle # 24
Survival Tactics - Find the Riddler Trophy for Caves Riddle # 20
Rumble in the Jungle - Find the Riddler Trophy for Caves Riddle # 9
Invisible Predator - Find the Riddler Trophy for Arkham Island, West Riddle #9
Intensive Treatment Extreme - Find the Riddler Trophy for The Penitentiary Riddle# 8
Silent knight (Extreme) - Find the Riddler Trophy for Botanical Gardens Riddle # 29
Sewer Bat Extreme - Find the Riddler Trophy for Intensive Treament Riddle # 30
Record Breaker (Extreme) - Find the Riddler Trophy for Caves Riddle# 19
Shock and Awe (Extreme) - Find the Riddler Trophy for Medical Riddle # 28
Survival Tactics (Extreme) - Find the Riddler Trophy for Mansion Riddle # 29
Rumble in the Jungle (Extreme) - Find the Riddler Trophy for Caves Riddle #23