In my opinion Batman should kill the Joker, obviously nothing else is working. The Joker escapes jail, Batman catches him and puts him back in and then the cycle repeats itself. ". . . he killed the second Robin. . . killed Lieutenant Sarah Essen." So it's pretty clear that the Joker's got some issues and after killing so many, it's oblivious that nothings going to change, therefore Batman should just kill him.