Originally Posted by BatFan1986
Batman didn't willingly go after Joker with a gun, he shot the grappling gun in an attempt to keep his ass on the roof. He never set out to kill Joker, it was never implied that he was going to as far as I remember, he beat the hell out of him on the church, yeah, and he said that he had to stop him but absolutely no indication that he'd kill Joker.
Actually, he obviously tried to kill him a couple times.
He blew up Axis Chemicals (and every goon inside), and you can assume he thought Joker was inside too.
But if that's not enough for you, he aims his Batwing machine guns and missiles DIRECTLY at the Joker.
Then, confronting him in the tower, he says "I'm going to kill you
" - before punching him right off the rooftop. Had Joker not held on, he'd have been dead right then.