Alternate costumes - Successfully complete the game to unlock the Caped Crusader, Dark Knight, and World's Greatest Detective costumes.
Batmobile missions - Successfully complete the Batmobile level to unlock the time attack and extra missions under the bonus option.
Defeating Ra's Al Goul - To defeat Ra's Al Goul at the end, make sure you defeat all of the ninjas that are around him; he will not die until all ninjas are dead. Also, when Ra's Al Goul is trying to attack you with the sword, it is best to use counter.
Movies and pictures - After completing certain levels, movies and pictures will be unlocked. This includes movie footage, interviews, and pictures.