You'll get this achievement near the end of Act 2. You'll have to actually kill her 3 times.
Don't try to kill her side kicks. It gives Black Cat an opportunity to hurt you and if you do kill them, they just respawn. Instead, focus on using Hyper-Sense often and go for 3 to 4 hit combos on Black Cat. Jump around often to counteract how much she jumps.
This is obviously much easier done on easy. If you have to, on the first and second times you have to kill her you can stand slightly off the platform that Black Cat stays on and use your Y attack (ranged) to kill her. Her and her side kicks won't come off the platform. Also, they are a few healing spheres around if you need one. Good luck!