Here is the full list of all 9 Galactic Core: The Lost Fleet achievements.
Finished the tutorial
Unlocked the Dual Gunner
Reached Wave 8 On The Rescue Mission
Unlocked the Engineer
Reached Wave 8 On The Survivors Mission
Finished Wave 4 With More Than 80% Accuracy
Killed more than 100 enemies in a single game
Killed a boss
Reached Level 10