Here is the full list of all 13 Starship Annihilator achievements.
It looks like you know what you're doing
This is a half way...
You killed the fourth, you are close to victory
Oh! This is the third one!
You have killed 666 enemies
Hey! You killed the second one.
You killed your first boss
You are the first
Soon it's over...
Mankind has a chance...
There were couple of steps...
You did it...
You saved mankind!