Here is the full list of all 24 Galactineers achievements.
Build a level 1 ship
Customize your player colour
Build a level 2 ship
Build a level 3 ship
Build a level 4 ship
Build a level 5 ship
Build 10 level 1 ships
Build 10 level 2 ships
Build 10 level 3 ships
Build 10 level 4 ships
Build 10 level 5 ships
Research a Caranum aspect
Research a Morgrax aspect
Research a Harv's aspect
Research a Pirates aspect
Research World Level 2
Research World Level 3
Research World Level 4
Research World Level 5
Use a Jump Portal with a ship
Produce an item in the foundry
Win a singleplayer PVE mission
Win a cooperative PVE mission
Win a PVP battle