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 more than 10,000,000,000 studs. (Single Player Only)
Complete 'Weathertop'.
Complete a level in co-op.
Defeat 42 Uruk-hai as Legolas.
Complete 'The Mines of Moria' in under 15 minutes.
Finish one of Gimli's opponents as Legolas in 'Helm's Deep'.
Unlock all the Map Stones in Middle-earth. (Single Player Only)
Defeat Gollum as Gollum.
Turn an enemy into a skeleton and make them dance.
During 'Prologue', jump into the fires of Mount Doom as Isildur.
Travel to Isengard as every playable Hobbit.
Get 100%. (Single Player Only)
Travel to Trollshaws as Bilbo.
Use the Ent Draught on Pippin.
Unlock all characters. (Single Player Only)
Craft every Mithril item. (Single Player Only)
Collect all the Mithril Bricks. (Single Player Only)
Dress a character completely in treasure items.
Equip Aragorn with the Mushroom Crown.
Complete all the Fetch Quests in Middle-earth. (Single Player Only)
Collect all the Red Bricks. (Single Player Only)
Craft the Fire and Ice Bows. (Single Player Only)
Fish perfectly 20 times by pressing the icon as it flashes.
Achieve True Adventurer in every level. (Single Player Only)
Complete 2 cooking puzzles.
Walk into Mordor.
Complete the Bonus Level.
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 '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'.
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 'The Black Rider'.
Complete 'Prologue'.