There are 12 Trophies that can be collected.

Bronze

Bounty Hunter
Complete all bounty side requests.

Collect 'em All
Unlock all special units.

Online Hero
Win a battle in 1 vs. 1 online mode.

Sir-Links-A-Lot
Create a link of 5+ formations in battle.

Fusion Fanatic
Triple fuse an attack formation in battle.

Team Player
Win a battle in 2 vs. 2 online COOP mode.

Young Hero
Win a battle in the Sylvan campaign.

Silver

Unstoppable Army
Reach a Hero level of 10 and max out all units to level 5 in any campaign.

Legend of Battles
Reach Level 10 in online multiplayer mode.

Skilled Strategist
Complete all Battle Puzzles in each Campaign.

Treasure Hunter
Collect all artifacts of each campaign.

Gold

Hero of Might and Magic
Complete all main quest and side quest objectives in all Campaigns.

http://www.ps3trophies.org/game/might-and-magic-clash-of-heroes/trophies/