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.
Travel to Trollshaws as Bilbo.
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)
Collect more than 10,000,000,000 studs. (Single Player Only)
Complete all the Fetch Quests in Middle-earth. (Single Player Only)
Throw Gimli 30 times.
Collect all the Red Bricks. (Single Player Only)
Achieve True Adventurer in every level. (Single Player Only)
Travel to Isengard as every playable Hobbit.
Turn an enemy into a skeleton and make them dance.
Craft the Fire and Ice Bows. (Single Player Only)
Defeat 42 Uruk-hai as Legolas.
Complete the Bonus Level.
Fish perfectly 20 times by pressing the icon as it flashes.
Defeat Gollum as Gollum.
Dress a character completely in treasure items.
Unlock all the Map Stones in Middle-earth. (Single Player Only)
Use the Ent Draught on Pippin.
Complete 2 cooking puzzles.
Equip Aragorn with the Mushroom Crown.
Complete 'Mount Doom'.
Complete 'The Black Gate'.
Walk into Mordor.
Complete 'Cirith Ungol'.
Complete 'The Secret Stairs'.
Complete 'The Battle of Pelennor Fields'.
Complete 'The Paths of the Dead'.
Defeat an Oliphaunt as Legolas.
Complete 'Osgiliath'.
Complete 'Helm's Deep'.
Finish one of Gimli's opponents as Legolas in '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'.
Complete a level in co-op.
Complete 'The Mines of Moria' in under 15 minutes.
During 'Prologue', jump into the fires of Mount Doom as Isildur.