Here is the full list of all 9 Bombernauts achievements.
Equip a sweet hat
Win a round of Bombernauts
The disciple gives tribute. (suggested by Hammerfan)
Enter orbit. (suggested by Mystic Asian)
Become the Duckmaster
Witness King Server winning a round of Bombernauts
Win a Saturday Special
Destroy the ENTIRE map, as a team!
Spread the good word of the Brain Slime