Here is the full list of all 13 WAKUSEI achievements.
Have four Earths at the same time
Create your first Sun
Destroy a Planet with the Death Laser
Unlock the Classic Mode
Unlock the Rush Mode
Unlock the Gravity Mode
Let a Blackhole consume a Planet
Collect a Comet
Unlock the last border expansion
Unlock the Foreshadow extra
Merge two suns together
Reach a combo multiplier of 25
Have one of each planet at the same time