Here is the full list of all 17 Cake Invaders achievements.
Launched the game for the first time.
First time clearing a wave.
Game over for the first time.
See the ranking for the first time.
Defeat the enemy for the first time.
Gaining skills for the first time
Increased crew to two.
Increase the crew to five.
Kill 50 of them with the increased damage of the bullets.
Shoot 200 bullets while the rate of fire is increased.
Kill two or more of them at once with a single laser shot.
Kill two or more of them at once with a single Dokkan bullet.
First time to reach 5 waves.
First time to reach 9 waves.
Reaching 10 waves without being able to eat a single baumkuchen.
Endure 3 waves with 1 layer of baumkuchen remaining.
Play a lot of Cake Invaders.