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