All you have to for this achievement is make sure you kill Bruce without killing Roo in Stage 2 of Streets of Rage 3. Roo has 2 bars of health, while Bruce has 3. As long as most of your attacks land on Bruce, you should be fine.
Bruce himself is very easy to fight. Your main problem is Roo. His jump attacks can easily stun you. Simply use
+
to jump kick him, doing a small amount of damage and stunning him. Just make sure you don't directly attack him. Once he's stunned, you'll have several seconds to attack Bruce. Rinse and repeat. Once you have Roo under control, it'll be very easy to defeat Bruce. Once he hops away to your left, you'll unlock the achievement.