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