There are 34 Trophies that can be collected.

Bronze

Hell of a Start
Finish the game on Normal Mode with any character.

Worst Kept Secret
Complete a Secret Mission with any character.

Blood, Sweat, and Tears
Pass 666 levels in Bloody Palace Mode.

Devilish Deed
Achieve an S Rank on any mission with any character.

Man's Best Friend
Defeat Cerberus.

Pest Control
Defeat Gigapede.

Double Trouble
Defeat Agni and Rudra.

Sibling Rivalry
Survive an encounter with Vergil.

Inside Out
Defeat the Heart of Leviathan.

Lightning In A Bottle
Defeat Nevan.

Lights Out
Defeat Beowulf.

Rough Rider
Defeat Geryon.

Brotherly Love
Fight Vergil a second time and prevail.

That's Not Lady-Like
Defeat Lady.

Step Into The Light
Defeat Doppelganger.

Asylum
Defeat Arkham.

Silver

Gone To Hell
Finish the game on Hard Mode with any character.

To Hell And Back
Finish the game on Very Hard Mode with any character.

Heaven Can Wait
Finish the game on Heaven or Hell Mode with any character.

Am I My Brother's Keeper
Finish the game on any difficulty as Vergil.

To Hell With That
Kill 100 enemies during the credits.

Blood Donor
Pass 5000 levels in Bloody Palace Mode.

Big Spender
Purchase all Devil Arm skills with Dante.

Who's Laughing Now?
Defeat Jester in all of his forms.

The Path Less Travelled
Clear every mission in Yellow Orb Mode.

Locked 'n Loaded
Reach the highest level for any gun with Dante.

Maximize Your Health
Max out the Health Bar with Dante.

Give 'em Hell
Max out the Devil Trigger Gauge with Dante.

Gold

Hell Hath No Fury…
Finish the game on Dante Must Die Mode with any character.

Left No Stone Unturned
Complete all Secret Missions with any Character.

Bloody Hell
Complete Bloody Palace Mode.

Hellish Honor
Achieve an S Rank on all missions (any difficulty or character).

Trend Setter
Reach the highest level in all Styles with Dante.

Platinum

Platinum Trophy
Unlock all trophies.

http://www.ps3trophies.com/forums/playstation-trophy-news/13879-devil-may-cry-3-hd-trophy-list.html

wolf-OF-chaos said:

These platinum's are going to be hard to get

agreed will give the first one a try see how I get on.