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