Here is the full list of all 48 LEGO The Lord of the Rings achievements. It takes around 30-35 hours to unlock all of the achievements on Windows.
Form The Fellowship of the Ring.
Defeat Gollum as Gollum.
Defeat an Oliphaunt as Legolas.
Finish one of Gimli's opponents as Legolas in 'Helm's Deep'.
Travel to Isengard as every playable Hobbit.
During 'Prologue', jump into the fires of Mount Doom as Isildur.
Get 100%. (Single Player Only)
Unlock all characters. (Single Player Only)
Craft every Mithril item. (Single Player Only)
Travel to Trollshaws as Bilbo.
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)
Fish perfectly 20 times by pressing the icon as it flashes.
Turn an enemy into a skeleton and make them dance.
Craft the Fire and Ice Bows. (Single Player Only)
Collect more than 10,000,000,000 studs. (Single Player Only)
Defeat 42 Uruk-hai as Legolas.
Reach the top of Amon Hen without being caught once by Boromir. (Single Player Only)
Complete a level in co-op.
Complete 'The Pass of Caradhras'.
Complete 'Weathertop'.
Complete 'The Mines of Moria'.
Complete 'The Mines of Moria' in under 15 minutes.
Achieve True Adventurer in every level. (Single Player Only)
Equip Aragorn with the Mushroom Crown.
Dress a character completely in treasure items.
Use the Ent Draught on Pippin.
Complete 2 cooking puzzles.
Throw Gimli 30 times.
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'.
Complete 'The Paths of the Dead'.
Walk into Mordor.
Complete 'Cirith Ungol'.
Complete 'The Secret Stairs'.
Complete 'Osgiliath'.
Complete 'Helm's Deep'.
Complete 'Warg Attack'.
Complete 'Track Hobbits'.
Complete 'Taming Gollum'.
Complete 'The Dead Marshes'.
Complete 'Amon Hen'.
Complete 'The Black Rider'.
Complete 'Prologue'.