Here is the full list of all 37 88 Heroes trophies - there are 23 bronze, 8 silver, 5 gold and 1 platinum.
Complete Magnificent 8 mode
Kill any hero 88 times
Kill every unique hero once
Collect 88 large coins
Destroy 88 blocks in a single game
Complete a level with zero seconds left on the clock
Collect 88 small coins
Finish with 8 minutes (or more) remaining on the Doomsday Timer
Complete the Space Station
Score 888,888 points
Complete the Volcano
32 Perfect rounds
Complete the Sewers
16 Perfect rounds
Kill any hero 8 times
Die 88 times
8 Perfect rounds
Complete the Office
Kill 88 enemies in one game
Complete any room in under 3 seconds
Score 88,888 points
Revive a hero
Collect 8 large coins
Collect 8 small coins
Die 8 times
Kill 8 enemies in one game
Die for the first time
Kill your first enemy
Score 8,888 points
Complete your first room
Unlock all trophies
Kill 888 enemies in total
Complete 88 Mode with 8 heroes remaining
Complete 88 Mode with 16 heroes remaining
Complete Solo mode
Play the game 88 times
Die 888 times