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