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