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.
Collect all the Red Bricks. (Single Player Only)
Craft the Fire and Ice Bows. (Single Player Only)
Complete 'The Mines of Moria' in under 15 minutes.
Equip Aragorn with the Mushroom Crown.
Use the Ent Draught on Pippin.
Fish perfectly 20 times by pressing the icon as it flashes.
Complete the Bonus Level.
Finish one of Gimli's opponents as Legolas in 'Helm's Deep'.
Turn an enemy into a skeleton and make them dance.
Travel to Isengard as every playable Hobbit.
Throw Gimli 30 times.
Defeat 42 Uruk-hai as Legolas.
Complete a level in co-op.
Complete 2 cooking puzzles.
Achieve True Adventurer in every level. (Single Player Only)
Dress a character completely in treasure items.
Unlock all the Map Stones in Middle-earth. (Single Player Only)
Travel to Trollshaws as Bilbo.
Defeat Gollum as Gollum.
Complete 'Mount Doom'.
Complete 'The Black Gate'.
Complete 'The Battle of Pelennor Fields'.
Defeat an Oliphaunt as Legolas.
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 '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 'Prologue'.
During 'Prologue', jump into the fires of Mount Doom as Isildur.
Collect all the Mithril Bricks. (Single Player Only)
Complete all the Fetch Quests in Middle-earth. (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)