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 without using any Yellow Orbs
Max out the Health Bar
Complete all Secret Missions
Finish the game on Dante Must Die Mode
Finish the Game on Hard Mode
Collect 50,000 Red Orbs
Complete six Secret Missions
Purchase all of Dante's Skills
Perform an S Rank Combo using Ifrit
Achieve an S Rank on any Mission
Clear a mission without taking damage
Finish the game on Normal Mode
Collect 25,000 Red Orbs
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
Complete a Secret Mission
Defeat Griffon
Collect all Guns
Collect 10,000 Red Orbs
Fight Griffon a second time and prevail
Fight Nelo Angelo a second time and prevail
Unlock 50% of all entries for every enemy file in the status menu
Perform an S Rank Combo using Alastor
Survive an encounter with Griffon
Defeat Phantom
Survive an encounter with Nelo Angelo
Survive an encounter with Phantom
Complete a Blue Orb