Here is the full list of all 16 8-Bit Commando achievements.
Complete any mission in coop
Complete at least one versus match
Complete every mission on hard difficulty
Complete the seventh mission
Complete the sixth mission
Take out 81 bad guys
Complete the fifth mission
Collect every type of powerup
Complete the fourth mission
Complete the third mission
Fire over 666 bullets
Complete any mission in under 2 minutes
Complete the second mission
Complete a mission without dying or losing any health
Complete the first mission