Here is the full list of all 34 Devil May Cry 2 HD trophies - there are 12 bronze, 17 silver, 4 gold and 1 platinum.
Finish the game on Hard Mode with any character
Reach Level 3 on any Gun with Dante
Collect 12 Blue Orb fragments (Dante/Lucia)
Pass 1000 levels in Bloody Palace Mode
Collect all Arsenals with Lucia
Defeat Tateobesu
Reach Level 3 on any Sword with Lucia
Perform an S Rank Combo using Lucia
Defeat Tartarussian
Finish the game on Normal Mode with any character
Defeat the final boss with either Dante or Lucia
Defeat Trismagia
Defeat Phantom
Collect all Swords with Dante
Defeat Plutonian
Defeat Bolverk
Defeat Noctpteran
Defeat Nefasturris
Perform an S Rank Combo using Dante
Defeat Jokatgulm
Defeat Orangguerra
Complete a Secret Mission
Unlock all trophies
Finish the game on Must Die Mode with any character
Finish the game on any difficulty with Trish
Pass 5000 levels in Bloody Palace Mode
Pass 9000 levels in Bloody Palace Mode
Achieve an S Rank on any Mission with Dante
Achieve an S Rank on any Mission with Lucia
Max out Health Bar with any character
Max out Devil Trigger Gauge with any character
Reach Level 3 on all Swords with Dante
Reach Level 3 on all Arsenals with Lucia
Collect all Devil Hearts with Lucia