Burton's Batman 3 was going to be about Batman's redemption. "Batman Forever" does cover this though. Batman was indeed a killer in the original film. He intentionally killed Joker and the thugs. In "Batman Returns", his bloodthirst had grown and he became more of an anti-hero. But some fans don't see the significance of the climax in that film. Batman refuses to kill Shreck and he tries to stop Selina from going down the same path as he did. At the masquerade ball, Bruce and Selina admit that they are tired of wearing masks. Batman later proves this when he tears his mask off, showing that he's losing his motivation to be Batman and he seeks redemption. But Selina rejects him and Bruce is left in a state of purgatory.
I doubt Burton would have made Batman kill anyone in his third film. It's quite clear that at the end of "Batman Returns", Bruce is no longer vengeful. In "Batman Forever", he tries to stop Robin from killing Two-Face and making the same mistake that he and Selina made. Unlike Selina, Robin listens to him and Batman is redeemed.