Here is the full list of all 34 Super Cyborg trophies - there are 20 bronze, 7 silver, 6 gold and 1 platinum.
Unlock all trophies
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 level-7 final boss
Complete the game on 'Easy' difficulty
Complete the game on 'Normal' difficulty
Complete the game on 'Hard' difficulty
Complete the game on any difficulty setting in coop mode
Complete the game on any difficulty setting with no deaths
Complete the game on 'Hard' difficulty with no deaths
Complete the game on any difficulty setting 2 times in a row
Complete the game on any difficulty setting using only default weapon
Die 100 times
Find all hidden power-ups
Steal a life from other player in coop mode
Use maximum charged fire for all weapons
Earn an extra life
Collect all power-ups in the game including all hidden power-ups
Earn 500000 score
Start the game as human
Don't kill the crawlers on level-2
Gather 10 walkers on the screen on level-6
Don't kill the tongue climbers at the elevator on level-7
Get squashed by the roof during the final boss encounter
Kill 10 enemies with one shot
Listen all tracks in music test menu (complete the game on 'Normal' difficulty to unlock it)