Here is the full list of all 41 Origin Space achievements.
Complete campaign Act I
Complete campaign Act II
Complete campaign Act III
Complete campaign Act IV
Complete 20 side quests
Complete 40 side quests
Complete 60 side quests
Complete all side quests
Gain 200000 credits
Play the game on 20 July
Play the game on 12 April
Destroy 100 enemy ships
Destroy 500 enemy ships
Destroy 2000 enemy ships
Destroy 10000 enemy ships
Destroy 10 elite enemies
Destroy 50 elite enemies
Destroy 200 elite enemies
Destroy 1000 elite enemies
Complete campaign on Hard difficulty
Complete campaign on Veteran difficulty
Complete campaign on Ace difficulty
Destroy the Cult Curator on Ace difficulty
Destroy Cerberus on Ace difficulty
Destroy Hierarch on Ace difficulty
Destroy Anima on Ace difficulty
Reach level 10
Reach level 20
Reach level 30
Reach level 40
Reach level 50
Reach level 60 playing as Sentinel
Reach level 60 playing as Scout
Reach level 60 playing as Engineer
Reach level 60 with all classes
Equip legendary fully equip your ship with level 60 legendary items
Upgrade your factory to Level 9
Produce a ship item in your factory
Upgrade your laboratory to level 9
Produce a ship item in your laboratory
Upgrade your warehouse to level 5