For this achievement, you must first unlock Brainiac by completing the story mode.
Now, enter any match with Brainiac (For ease, I prefer either a vs match against a second controller, or a single fight against an AI opponent on very easy). Get their health down to just a sliver, then use Brainiac's Character ability (B) to launch low damage missiles (Beta Strikes) at your opponent. When they go down from this attack, you will get the achievement.