Here is the full list of all 46 Psycho Starship Rampage achievements.
Destroy 100 ship carcasses
Build a ship with 100 total power
Build a ship of 100 tiles
Build a ship of 50 tiles
Survive level 0
Kill 200 enemies with shield
Kill 5000 enemies
Kill 300 enemies behind you in one run
Fire 100 mines
Destroy 100 asteroids
Kill 100 enemies using a tractor beam
Kill 500 enemies using a pulse emitter
Ram and kill 50 enemies
Survive level 10
Collect 30 life upgrades
Collect 20000 scrap
Build a ship with 20 cannons
Build a ship with 500 total power
Fire 100 torpedoes
Die 20 times
Survive level 20
Build a ship with 2000 total power
Kill 30000 enemies
Collect 50000 scrap
Kill 1000 enemies behind you
Collect 500 power-ups
Destroy 300 asteroids
Kill 5000 enemies using a laser cannon
Kill 10000 enemies using a laser cannon
Kill 1000 enemies using a pulse emitter
Destroy 200 ship carcasses
Survive level 30
Kill 500 enemies with shield
Fire 100 shockwaves
Kill 300 enemies using a tractor beam
Fire 30 black holes
Get hit 20 times by friendly fire
Fire 300 torpedoes
Kill 500 enemies using mines
Fire 100 subspace bubbles
Get hit 50 times by friendly fire
Absorb 100 plasma bullets with a shield
Ram and kill 500 enemies
Hack 200 loot boxes
Cancel 10000 enemy plasma bullets
Cancel 20000 enemy plasma bullets