Here is the full list of all 30 Space Will:Prologue achievements.
Clearing the Alpha Galaxy
Clearing the Beta Galaxy
First synthesis unit
Defeat any leader within 15 seconds
End the battle with 1 health point
The highest level reaches level 10
The highest level reaches level 20
Accumulated exploration completed once
Accumulated 2 explorations completed
Accumulated 3 explorations completed
Accumulated 5 explorations completed
Accumulated 8 explorations completed
Accumulated 10 explorations completed
Equip 10 units simultaneously
Equip 20 units simultaneously
Equip 30 units simultaneously
Defeat the "The Great Snake" once
Defeat the "Cosmic Ray Cruiser" once
Defeat the "Satellite" once
Use the "Warrior" to clear the level once
Use the "Apostle" to clear the level once
Use "Parallel envoy" to clear the level once
Use the "Sagittarius" to clear the level once
Use "God of War" to clear the level once
Use the "Dragonfly" to clear the level once
Use the "Gyro Voyager" to clear the level once
Use the "Newbie Vessel" account to clear the level once
Use the "Omnipotent Craft" to clear the level once
Use the "Quantum Vessel" to clear the level once