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