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)
Complete all the Fetch Quests in Middle-earth. (Single Player Only)
Collect all the Red Bricks. (Single Player Only)
Turn an enemy into a skeleton and make them dance.
Craft the Fire and Ice Bows. (Single Player Only)
Throw Gimli 30 times.
Achieve True Adventurer in every level. (Single Player Only)
Travel to Trollshaws as Bilbo.
Fish perfectly 20 times by pressing the icon as it flashes.
Travel to Isengard as every playable Hobbit.
Equip Aragorn with the Mushroom Crown.
Dress a character completely in treasure items.
Complete 2 cooking puzzles.
Collect more than 10,000,000,000 studs. (Single Player Only)
Use the Ent Draught on Pippin.
Walk into Mordor.
Defeat Gollum as Gollum.
Complete the Bonus Level.
Complete 'Mount Doom'.
Complete 'The Black Gate'.
Unlock all the Map Stones in Middle-earth. (Single Player Only)
Complete 'Cirith Ungol'.
Complete 'The Secret Stairs'.
Complete 'The Battle of Pelennor Fields'.
Defeat an Oliphaunt as Legolas.
Complete 'The Paths of the Dead'.
Complete 'Osgiliath'.
Complete 'The Dead Marshes'.
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 'Taming Gollum'.
Complete 'The Mines of Moria' in under 15 minutes. (Story Only)
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'.
Complete a level in co-op. (Story only)
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.