This is how to get the 'Who Needs Curiosiy?' achievement in Lego Batman for XBox 360.

Details: Defeat Catwoman 9 times.

This one may seem like a pain, since Catwoman is the boss of Chapter 2: Area 1 - Hero, but there is an easier (and I think the only) way to get it. To use her, you need to have completed Chapter 2 - Hero.
Once you have her available, head to Chapter 2: Area 2 - Villain.
Switch to The Penguin and start wailing on her.
9 kills should do it.