Here is the full list of all 49 LEGO The Lord of the Rings trophies - there are 40 bronze, 5 silver, 3 gold and 1 platinum.
Collect every trophy.
Get 100%. (Single Player Only)
Craft every Mithril item. (Single Player Only)
Collect all the Mithril Bricks. (Single Player Only)
Complete all the Fetch Quests in Middle-earth. (Single Player Only)
Collect more than 10,000,000,000 studs. (Single Player Only)
Travel to Trollshaws as Bilbo.
Complete a level in co-op. (Story only)
Reach the top of Amon Hen without being caught once by Boromir. (Single Player Only)
Collect all the Red Bricks. (Single Player Only)
Unlock all characters. (Single Player Only)
Complete the Bonus Level.
Travel to Isengard as every playable Hobbit.
Achieve True Adventurer in every level. (Single Player Only)
Complete 'Mount Doom'.
Complete 'The Black Gate'.
Unlock all the Map Stones in Middle-earth. (Single Player Only)
Fish perfectly 20 times by pressing the icon as it flashes.
Defeat Gollum as Gollum.
Complete 'The Battle of Pelennor Fields'.
Defeat an Oliphaunt as Legolas.
Craft the Fire and Ice Bows. (Single Player Only)
Walk into Mordor.
Complete 'Cirith Ungol'.
Complete 'The Paths of the Dead'.
Complete 'The Secret Stairs'.
Use the Ent Draught on Pippin.
Complete 'Osgiliath'.
Defeat 42 Uruk-hai as Legolas.
Complete 'Helm's Deep'.
Finish one of Gimli's opponents as Legolas in 'Helm's Deep'.
Dress a character completely in treasure items.
Complete 'Warg Attack'.
Throw Gimli 30 times.
Turn an enemy into a skeleton and make them dance.
Complete 'Track Hobbits'.
Complete 'The Dead Marshes'.
Complete 'Taming Gollum'.
Equip Aragorn with the Mushroom Crown.
Complete 2 cooking puzzles.
Complete 'The Mines of Moria' in under 15 minutes. (Story Only)
Complete 'Amon Hen'.
Complete 'The Mines of Moria'.
Complete 'The Pass of Caradhras'.
Form The Fellowship of the Ring.
Complete 'Weathertop'.
Complete 'The Black Rider'.
Complete 'Prologue'.
During 'Prologue', jump into the fires of Mount Doom as Isildur.