It could be argued that he killed in BATMAN. We know he uses lethal force, though we never really see anyone actually die, as I recall. Batman's actions did lead to The Joker's death, but Joker had every opportunity not to hang onto that ladder and buck the laws of physics.
He uses lethal force and likely kills in BATMAN RETURNS, though again, any deaths are offscreen.
But in BATMAN FOREVER, Batman did not kill Two-Face. Throwing a handful of coins into the air, even if you know the person will try to catch them, is not killing someone. Did he take advantage of Two-Face's compulsion? Sure, to distract him, but Two-Face is the idiot who reached out and stepped off the ledge.
I don't remember him killing in BATMAN & ROBIN.
In BATMAN BEGINS, he caused a series of explosions and a fire that likely led to deaths, but again, offscreen. And he refused to save Ra's Al Ghul after James Gordon blew out the tracks. I don't think you can argue he killed him, though not offering the chance for life is out of character for Batman.