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