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