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