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