Here is the full list of all 15 Cute Invaders achievements.
Clear the Campaign
Rescue one commander
Rescue all commander
Clear the campaign without using auto-aim
Achieve level 10.
Kill a monster
Kill 10 monster
Kill a grade B monster
Kill a grade A monster
Kill a grade S monster
First defeat
First K.I.A
Adjusting the BGM volume.
Complete the Tutorial
Change Controls.