Here is the full list of all 35 Super Cyborg achievements.
Earn an extra life
Destroy level-1 boss
Destroy level-2 boss
Destroy level-3 miniboss
Destroy level-3 boss
Destroy level-4 miniboss
Destroy level-4 boss
Destroy level-5 miniboss
Destroy level-5 boss
Destroy level-6 boss
Destroy level-7 boss
Destroy everything
Complete the game on 'Easy' difficulty setting
Complete the game on 'Normal' difficulty setting
Complete the game on 'Hard' difficulty setting
Complete the game on any difficulty setting with no deaths
Complete the game on any difficulty setting 2 times in a row
Complete the game on any difficulty setting using only alternate firing
Complete the game on 'Hard' difficulty setting with no deaths
Complete the game on any difficulty setting in coop mode
Complete the game on any difficulty setting in coop mode without any single shot and deaths from player 2
Die 100 times
Find all hidden power-ups
Steal a life while playing coop mode
Use maximum charged alternate fire for all weapons
Collect all power-ups in the game (including all hidden power-ups)
Earn 500000 points
Gather 10 quadropods on the screen on level 6
Kill 10 enemies with one shot
Listen all tracks in music test menu (Complete the game to unlock it)