Mr. Freeze: You will bring me Nora or you will die.
Professor Hugo Strange: I feel I should thank you, capturing Bruce Wayne is so much easier than Batman.
Batman: It was all a lie. There's nothing wrong with you.
Joker: Nice of you to say. But you of all people should know there's plenty wrong with me.
Answer: Batman later in the game discovers that Hugo Strange has been supplying everybody with weapons, so he would have given Two-Face the vat of acid.