We all know Batman & Robin, but you'd be surprised that anyone could get a Moment of Awesome from this film. And surprisingly, it's Mr. Freeze who earns it, in his final scene where he confronts Ivy in Arkham, after learning that Ivy had nearly killed his wife. (According to the novel, he traded the cure for his wife's disease just so he could share the cell.) His dialogue is just plain and simply chilling and Badass, and no review of the movie can deny it.
Mr. Freeze: Surprise. I am your new cellmate, and I've come to make your life a living hell. Prepare for a bitter harvest; winter has come at last.
Mr. Freeze's capture right after he crashed the auction.
Robin out gambiting Poison Ivy. Say what you will about the rest of the movie, but that's an awesome moment. And while she has a chance to do it again after taking the rubber lips off, she drowns him instead. Clearly too pissed to notice.
For all the film's flaws, the movie does come closest out of the four films to portraying a father-son dynamic between Bruce and Alfred, especially the scenes where Alfred talks to Bruce about his stubborn nature in the Batman persona and the scene on Alfred's near-deathbed.