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