Poison Ivy = Lady Macbeth?
Throughout the film, Poison Ivy give a few asides (Observatory, Turkish Baths, Nora's chamber etc.), making her character more of a Shakespearean tragic villain. Additionally, she manipulates Mr. Freeze, similar to Lady Macbeth's manipulation of Macbeth. Finally, both Poison Ivy and Lady Macbeth make their male counterparts realize their true potential, and both have an early end (Lady Macbeth's death, Ivy's defeat).
Does anyone else share this perspective, or perhaps a counter-argument?