Here is the full list of all 29 Beyond Space achievements.
Complete tutorial
Destroy 50 enemy ships using Plasma Blaster weapon type.
Destroy 50 enemy ships using Donkey Shot.
Destroy 20 enemy ships using Hammer.
Destroy 20 enemy ships using Firefly.
Destroy 20 enemy ships using Fatty.
Destroy 20 enemy ships using Swissman.
Destroy 20 enemy ships using Needle or Saber.
Complete mission with full armor.
Fire all Donkey Shot missles.
Unlock all weapons
Unlock all ships.
Customize a ship.
Complete mission using only one type of weapon.
Get destroyed 5 times in a single mission.
Defeat final boss.
Deafeat Lado
Defeat two corvettes.
Complete mission 1
Complete mission 2
Complete mission 4
Complete mission 6
Complete mission 7
Complete mission 11
Complete mission 15
Complete mission 16
Finish game on Relax difficulty.
Finish game on Normal difficulty.
Finish game on Nightmare difficulty.