You can get this achievement either in the Story Mode of Villain level 2-5 (Stealing the Show, where you play as Catwoman and The Penguin), or in any level's Free Play after having unlocked Catwoman by completing Villian level 2-5 (just switch one character to Catwoman during Free Play). I actually got this by accident during Story Mode, because I had bad aim with Penguin Bombers. :-/
Either way, kill your Catwoman character 9 times to earn the achievement. This will be fastest if you use one-hit kills. For example, The Penguin has Penguin Bombers. Alternatively, in Free Play, the super-strength attack of Bane, Clayface, Killer Croc, Mr. Freeze, and Man-Bat works, too.