Beat the game and continue through the same save.
You must have unlocked hard mode first. You have to collect the 16 bat symbols on your second run through the game.
Successfully complete the game to unlock the Caped Crusader, Dark Knight, and World's Greatest Detective costumes.
Successfully complete the Batmobile level to unlock the time attack and extra missions under the bonus option.
After completing certain levels, movies become unlocked. This includes movie footage and interviews.