Here is the full list of all 14 Astro Duel achievements.
Collect 1000 powerups
Score a triple kill
Win in Overtime
Unlock Triple Powerups
Destroy every block on the Cache level
Escape the Black Hole
Destroy the Turret
Win with 2 extra points
Defeat 3 hard computers in a free-for-all
Kill four ships at once
Run over 10 pilots in Pilot Execution mode
Win a 1v1 against the computer
Respawn 3 times in a single round
Use gravity to guide a killing bullet