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