Here is the full list of all 34 Devil May Cry HD trophies - there are 20 bronze, 7 silver, 6 gold and 1 platinum.
Unlock all trophies
Unlock all the entries for every enemy file in the status menu
Finish the game on Dante Must Die Mode
Finish the Game on Hard Mode
Purchase all of Dante's Skills
Max out the Health Bar
Complete all Secret Missions
Collect 50,000 Red Orbs
Finish the game without using any Yellow Orbs
Finish the game on Normal Mode
Defeat Mundus
Unlock every enemy file in the status menu
Defeat Nightmare
Fight Nightmare a second time and prevail
Defeat Nelo Angelo
Survive an encounter with Nightmare
Collect 25,000 Red Orbs
Defeat Griffon
Collect all Guns
Complete six Secret Missions
Fight Griffon a second time and prevail
Fight Nelo Angelo a second time and prevail
Perform an S Rank Combo using Ifrit
Unlock 50% of all entries for every enemy file in the status menu
Survive an encounter with Griffon
Defeat Phantom
Collect 10,000 Red Orbs
Clear a mission without taking damage
Survive an encounter with Nelo Angelo
Achieve an S Rank on any Mission
Survive an encounter with Phantom
Complete a Secret Mission
Perform an S Rank Combo using Alastor
Complete a Blue Orb