He tried to kill Batman . And almost thought he did. So it was self defense. It wasn't cheap. This guy was trying to kill him. You see how he was trying to take Batman's head off when he swung at him with the chains like three or four times. Batman was injured bad and didn't have time for games . The only thing that was on his mind other than staying alive was to kill the man that killed his parents which in this case was the Joker.You saw how he took the first guy out that was backflipping toward him with knives on his boots. Batman was driven to take down the Joker and nobody was going to stop him even in his weak condition . Would you rather have the thug look down for Batman. Then the thug feels and sees Batmans shadow behind him. Then gets startled and starts falling off the ledge . Then Batman says to the thug as he's falling, "I don't have to kill you , but I don't have to save you. " Lame.