There are eight bonus costumes (aka skins) to unlock in Batman: Arkham Origins, and even more pre-order and DLC costumes.
Here are the costumes that you can unlock via regular methods, and how to unlock them.
Blackest Night – Earn Prestige in Multiplayer mode
Dark Knight – Complete all Dark Knight challenges
Earth 2 Dark Knight – Connect your WBID to the Batman: Arkham Origins mobile game
Injustice – Earn all medals in Challenge mode
New 52 – Complete all Most Wanted missions by capturing all Most Wanted targets
Noel – Find all Enigma Datapacks
One Million – Register and link a WBID account
Red Son – Connect your WBID to the Batman: Arkham Origins mobile game, and unlock ten costumes in the mobile game
Check out my full guide for the complete list of unlockable, pre-order, and DLC costumes.