Here is the full list of all 13 Dustforce trophies - there are 9 bronze, 3 silver and 1 gold.
Score a flawless victory in a four-player online match
Score double-S in all original single player levels
Sweep 50 apples
Pass a red level without respawning
Unlock all Laboratory levels
Score double-S in all combat levels without using area attack
Score double-S in a silver level in each hub
Unlock all City levels
Unlock all Mansion levels
Use area attack three times in a single player level
Unlock all Forest levels
Obtain a red key
Obtain a gold key