Here is the full list of all 13 Cubetractor achievements.
Complete all quests.
Acquire all the stars.
Complete all examinations with a Gold rating or higher.
Complete all examinations with a Master rating
Complete all examinations.
Build 10 structures within a period of 9 seconds.
Build 8 structures within a period of 6 seconds.
Destroy 3 enemy critters with one cube.
Kill 7 enemy critters within a period of 5 seconds.
Complete 4 examinations with a Master rating.
Complete 4 examinations with a Gold rating or higher.
Have 13 Cubes moving at the same time while being chased by a Homing Missile.
Build 4 structures within a period of 3 seconds.