Here is the full list of all 34 Devil May Cry 3 HD trophies - there are 16 bronze, 12 silver, 5 gold and 1 platinum.
Unlock all trophies.
Achieve an S Rank on all missions (any difficulty or character).
Clear every mission in Yellow Orb Mode.
Finish the game on any difficulty as Vergil.
Complete Bloody Palace Mode.
Pass 5000 levels in Bloody Palace Mode.
Pass 666 levels in Bloody Palace Mode.
Finish the game on Heaven or Hell Mode with any character.
Finish the game on Dante Must Die Mode with any character.
Finish the game on Very Hard Mode with any character.
Finish the game on Hard Mode with any character.
Reach the highest level in all Styles with Dante.
Purchase all Devil Arm skills with Dante.
Kill 100 enemies during the credits.
Max out the Health Bar with Dante.
Complete all Secret Missions with any Character.
Max out the Devil Trigger Gauge with Dante.
Achieve an S Rank on any mission with any character.
Finish the game on Normal Mode with any character.
Defeat Arkham.
Defeat Doppelganger.
Defeat Jester in all of his forms.
Defeat Lady.
Fight Vergil a second time and prevail.
Defeat Geryon.
Defeat Beowulf.
Defeat Nevan.
Defeat the Heart of Leviathan.
Survive an encounter with Vergil.
Reach the highest level for any gun with Dante.
Defeat Agni and Rudra.
Defeat Gigapede.
Defeat Cerberus.
Complete a Secret Mission with any character.