There are 57 Trophies that can be collected.

Bronze

Smithy    
You upgraded your first equipment. Keep it up!    

This Is My Weapon    
You upgraded an Equipment to its maximum potential!    

Obedience Training    
You raised a Pet to its maximum potential!    

Pupil    
Reached Hero Level 10    

Veteran     
Reached Hero Level 30     

Defender of Etheria    
Reached Hero Level 70    

To The Limit    
Wore a complete set of maximum level Equipments  

From The Depths    
Completed all Area 1 levels on any difficulty setting    

To The Rooftops    
Completed all Area 2 levels on any difficulty setting    

A Taste of Victory    
Completed all Area 3 levels on any difficulty setting    

Dungeon Crawler    
Completed all levels on any difficulty setting    

The Belly of the Beast    
Completed all Area 1 levels on Hard    

The Body of the Beast    
Completed all Area 2 levels on Hard    

The Crown of the Beast    
Completed all Area 3 levels on Hard

From Fire with Brimstone    
Completed all Area 1 levels on Insane    

Through The Crowded Keep    
Completed all Area 2 levels on Insane    

To The Lofty Summit    
Completed all Area 3 levels on Insane

Where's the Blueprints?    
Completed No Towers Allowed on >= Medium Difficulty    

Friends Forever    
Completed Unlikely Allies on >= Medium Difficulty    

88 Core    
Completed Warping Core on >= Medium Difficulty    

Ella, Ella    
Completed Raining Goblins on >= Medium Difficulty    

Wizard Hunter    
Completed Wizardry on >= Medium Difficulty    

You No Take Mushroom    
Completed Ogre Crush on >= Medium Difficulty    

Speed Freak    
Completed Zippy Terror on >= Medium Difficulty    

In A Fowl Mood    
Completed Chicken on >= Medium Difficulty    

Core Cardio    
Completed Moving Core on >= Medium Difficulty    

Monster Mania    
Completed Death From Above on >= Medium Difficulty    

Core Destroyer    
Completed Assault on >= Medium Difficulty    

Gold Rush    
Completed Treasure Hunt on >= Medium Difficulty

Survivalist    
Reached Survival Wave 15 on Medium Difficulty    

Thick Skin    
Reached Survival Wave 20 on Medium Difficulty    

Tough Guy    
Reached Survival Wave 15 on Hard Difficulty    

Iron Man    
Reached Survival Wave 10 on Insane Difficulty    

Defense Is the Best Offense    
Reached Wave 10 on all levels in Pure Strategy on >= Medium Difficulty    

True Nobility    
Earned the Lord Award on >= Medium Difficulty    

O Mighty Smiter!    
Wore a full set of Godly Items    

Divine Intention    
Picked up a Godly Weapon    

Perfectionist    
Earned the Flawless Victory Award on at least 6 Missions on >= Normal Difficulty    

Daredevil    
Earned Skin of Your Teeth Award on 6 Missions    

Mastermind    
Earned the Master Strategist Award on all Missions    

Brute Force    
Earned the Gunslinger Award on all Missions    

Team Effort    
Completed all levels with 4 active players on >= Medium Difficulty    

A Matter of Perspective    
Saw all four Hero endings

Catch 'em All    
Stored all Familiar types in your Item Box or on your Heroes    

Master Banker    
Stored 15,000,000 Mana in your Mana Bank    

Good Student    
Completed the Tutorial. You deserve a cookie!

Silver

Dungeon Raider    
Completed all levels on Hard

A Challenger Approaches    
Completed All Challenges on INSANE Difficulty!    

Weapon Master    
Completed No Towers Allowed on Insane Difficulty    

Kobold Exterminator    
Completed Zippy Terror on Insane Difficulty    

Monster Madness    
Completed Death From Above on Insane Difficulty    

Dancing in the Rain    
Completed Raining Goblins on Insane Difficulty    

Gold Blitz    
Completed Treasure Hunt on Insane Difficulty    

Ogre Block Party    
Completed Ogre Crush on Insane Difficulty

Group Hug    
Raised a Hero of each type to Level 70

Gold

Dungeon Defender    
Completed all levels on Insane! Congratulations Brave Dungeon Defender!

Platinum

Legendary Defender    
You have earned every Dungeon Defenders Accomplishment! Trendy salutes you!

http://www.ps3trophies.org/game/dungeon-defenders/trophies/