Here is the full list of all 40 LEGO The Hobbit trophies - there are 27 bronze, 8 silver, 4 gold and 1 platinum.
Collect every trophy
Achieve 100% completion
Complete all the quests in Middle-earth. (Single Player Only)
Collect all characters. (Single Player Only)
Forge all the Mithril Treasure Items. (Single Player Only)
Forge all the Perfect Mithril Treasure Items. (Single Player Only)
Collect all Mithril Bricks. (Single Player Only)
Collect 10,000,000,000 studs. (Single Player Only)
Collect all Schematics. (Single Player Only)
Collect all Minikits. (Single Player Only)
Collect all Treasure Items in levels. (Single Player Only)
Equip yourself with Dazzle Wig, Mithril Rhythm Stick and Mithril Dance Boots.
Use every Dwarf from Thorin's Company in a Buddy-Up attack
Use 50 Buddy-Up attacks
Obtain all Master Burglar titles. (Single Player Only)
Equip Thorin with the Mithril Mushroom Crown
Complete the mining game perfectly 50 times
Obtain 150,000 studs from Instruction Builds bonuses. (Single Player Only)
Transform to Beorn's bear form.
Complete the Bonus Level
Use Gandalf's startle ability to dazzle 50 enemies
Complete ''Inside Information''
Complete ''On the Doorstep''
Complete ''The Necromancer''
Complete ''Looking for Proof''
Complete ''A Warm Welcome''
Complete ''Barrels Out of Bond''
Complete ''Flies and Spiders''
Create a custom character.
Complete ''Queer Lodgings''
Complete ''Out of the Frying Pan…''
Complete ''Goblin Town''
Complete ''Over Hill and Under Hill''
Complete ''The Troll Hoard''
Collect 99 of any loot
Complete ''Roast Mutton''
Complete ''Azog the Defiler''
Complete ''An Unexpected Party''
Play a level in co-op
Complete ''Greatest Kingdom in Middle-earth''