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