Supposedly he was very difficult to work with during Forever. Shumacher frequently butted heads with him.
I actually read an interview with Shumacher - who, it must be said, comes across as a very nice man, whatever you think of his films - in which he said in all sincerity that Kilmer was clearly a very disturbed individual who needed help. I've also heard him say:
He was being irrational and ballistic with the first assistant director, the cameraman, the costume people," Schumacher told Entertainment Weekly. "He was rude and inappropriate. He was childish and impossible. I was forced to tell him that this would not be tolerated for one more second. Then we had two weeks where he did not speak to me but it was bliss!"
Certainly, around the same time, The Island of Doctor Moreau, in which Kilmer also appeared, led to numerous stories about what a nightmare he was on set, so Shumacher may have had some point here. Indeed, it was Shumacher who personally cast Kilmer in Batman Forever.