Here is the full list of all 204 Space Stories: Darth Star achievements.
Complete level 31
Kill 10x "Annihilator II"
Kill 10x "Annihilator"
Kill 1x "FlyDeath"
Kill 1x "Annihilator II"
Kill 1x "Annihilator"
Complete level 30
Kill 100x "Daredevil III"
Kill 100x "GrimFighter III"
Kill 1x "FlyDeath III"
Complete level 29
Kill 100x "GrimFighter"
Complete level 28
Complete level 27
Kill 100x "Fearless III"
Complete level 26
Kill 100x "GrimFighter II"
Complete level 25
Kill 10x "GrimFighter III"
Complete level 24
Kill 1x "GrimFighter III"
Complete level 23
Kill 10x "Daredevil III"
Kill 100x "Daredevil II"
Kill 100x "Daredevil"
Kill 1x "StarLeader II"
Kill 10x "GrimFighter"
Kill 1x "Daredevil III"
Complete level 22
Kill 10x "GrimFighter II"
Kill 1x "GrimFighter"
Kill 1x "GrimFighter II"
Complete level 21
Kill 10x "Daredevil II"
Kill 10x "Daredevil"
Kill 1x "StarLeader"
Kill 1x "Daredevil II"
Kill 1x "Daredevil"
Complete level 20
Kill 1x "StarLeader III"
Complete level 19
Complete level 18
Complete level 17
Kill 10x "Fearless III"
Kill 1x "Adamantine II"
Complete level 16
Complete level 15
Kill 1x "Fearless III"
Complete level 14
Kill 100x "Fearless II"
Kill 100x "Fearless"
Complete level 13
Complete level 12
Kill 1x "Adamantine"
Complete level 11
Kill 10x "Fearless II"
Kill 10x "Fearless"
Kill 1x "Fearless II"
Kill 1x "Fearless"
Complete level 10
Kill 1x "Adamantine III"
Complete level 9
Kill 100x "Light of Redemption III"
Complete level 8
Kill 10x "Light of Redemption III"
Kill 100x "Light of Redemption II"
Kill 1x "Light of Redemption III"
Complete level 7
Complete level 6
Complete level 5
Kill 10x "Light of Redemption II"
Complete level 4
Kill 1x "Light of Redemption II"
Complete level 3
Buy "Energy Shield Regeneration Speed III" upgrade
Buy "Energy Shield Regeneration Speed IV" upgrade
Buy "Energy Shield Regeneration Speed I" upgrade
Buy "Energy Shield Regeneration Speed II" upgrade
Buy "Energy Shield Count III" upgrade
Buy "Energy Shield Count IV" upgrade
Buy "Energy Shield Count I" upgrade
Buy "Energy Shield Count II" upgrade
Buy "Drone Power IV" upgrade
Buy "Drone Power III" upgrade
Buy "Drone Power I" upgrade
Buy "Drone Power II" upgrade
Buy "Drone Count I" upgrade
Buy "Drone Count II" upgrade
Buy "Drone Count III" upgrade
Buy "Drone Count IV" upgrade
Buy "Economic Center Speed II" upgrade
Buy "Economic Center Speed III" upgrade
Buy "Economic Center Speed IV" upgrade
Buy "Economic Center Speed I" upgrade
Buy "Economic Center Profit II" upgrade
Buy "Economic Center Profit III" upgrade
Buy "Economic Center Profit IV" upgrade
Buy "Economic Center Profit I" upgrade
Buy "Automatic Turret Speed I" upgrade
Buy "Automatic Turret Speed II" upgrade
Buy "Automatic Turret Speed III" upgrade
Buy "Automatic Turret Speed IV" upgrade
Buy "Automatic Turret Power III" upgrade
Buy "Automatic Turret Power IV" upgrade
Buy "Automatic Turret Power II" upgrade
Buy "Automatic Turret Power I" upgrade
Buy "Weapon VIII"
Buy "Weapon VII"
Buy "Weapon VI"
Buy "Weapon V"
Buy "Weapon IV"
Buy "Weapon III"
Buy "Weapon II"
Buy "Weapon I"
Build "Energy Shield"
Build "Hangar"
Build "Economic Center"
Build "Automatic Turret"
Complete level 2
Kill 100x "Light of Redemption"
Complete level 1
Kill 10x "Light of Redemption"
Kill 1x "Light of Redemption"
Complete level 32
Complete level 33
Complete level 34
Complete level 35
Complete level 36
Complete level 37
Complete level 38
Complete level 39
Complete level 40
Complete level 41
Complete level 42
Complete level 43
Complete level 44
Complete level 45
Complete level 46
Complete level 47
Complete level 48
Complete level 49
Kill 10x "Annihilator III"
Kill 10x "MegaAnnihilator"
Kill 10x "MegaAnnihilator II"
Kill 10x "MegaAnnihilator III"
Kill 10x "MadStar"
Kill 10x "MadStar II"
Kill 10x "MadStar III"
Kill 10x "WayFarer"
Kill 10x "WayFarer II"
Kill 10x "WayFarer III"
Kill 10x "Dragonfly"
Kill 10x "Dragonfly II"
Kill 10x "Dragonfly III"
Kill 10x "Invincible light"
Kill 10x "Invincible light II"
Kill 10x "Invincible light III"
Kill 100x "Annihilator"
Kill 100x "Annihilator II"
Kill 100x "Annihilator III"
Kill 100x "MegaAnnihilator"
Kill 100x "MegaAnnihilator II"
Kill 100x "MegaAnnihilator III"
Kill 100x "MadStar"
Kill 100x "MadStar II"
Kill 100x "MadStar III"
Kill 100x "WayFarer"
Kill 100x "WayFarer II"
Kill 100x "WayFarer III"
Kill 100x "Dragonfly"
Kill 100x "Dragonfly II"
Kill 100x "Dragonfly III"
Kill 100x "Invincible light"
Kill 100x "Invincible light II"
Kill 100x "Invincible light III"
Kill 1x "Annihilator III"
Kill 1x "MegaAnnihilator"
Kill 1x "MegaAnnihilator II"
Kill 1x "MegaAnnihilator III"
Kill 1x "MadStar"
Kill 1x "MadStar II"
Kill 1x "MadStar III"
Kill 1x "WayFarer"
Kill 1x "WayFarer II"
Kill 1x "WayFarer III"
Kill 1x "Dragonfly"
Kill 1x "Dragonfly II"
Kill 1x "Dragonfly III"
Kill 1x "Invincible light"
Kill 1x "Invincible light II"
Kill 1x "Invincible light III"
Kill 1x "FlyDeath II"
Kill 1x "Exterminator"
Kill 1x "Exterminator II"
Kill 1x "Exterminator III"
Kill 1x "StrongFaith"
Kill 1x "StrongFaith II"
Kill 1x "StrongFaith III"