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