Ion's right... Joker would never kill THE BATMAN. They have a deep link and Joker would just have no reason to live without Batman.
The only times he'd have killed a Batman is when it's not Bruce: trust me, he could tell easily. He would kill Dick, Jason or JP but NEVER THE BATMAN! He's ruin Gotham but Bruce would work out a weakness... he ain't stupid. I mean, Joker's the guy who won't unmask Bruce because it takes away from the whole "game"!