Defeat an opponent with a Hyper Combo 30 times to earn this achievement. You can make this easier on yourself by setting the difficulty to Easiest, the damage to Highest, and using Team Aerial Combos to raise your gauge bar.
When you have at least one gauge bar push two attack buttons simultaneously to perform a Hyper Combo, but make sure the enemies health is low. Repeat 30 times.
You can also build your gauge up to 2 or 3 in order to get the Galactic Smasher achievement as well. Simply hit both assist buttons when your gauge is at 2 or 3 to utilize your opponents Hyper Combos too.