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 a level in co-op.
Complete 'The Mines of Moria' in under 15 minutes.
Dress a character completely in treasure items.
Get 100%. (Single Player Only)
Collect all the Red Bricks. (Single Player Only)
Complete all the Fetch Quests in Middle-earth. (Single Player Only)
Unlock all characters. (Single Player Only)
Craft every Mithril item. (Single Player Only)
Collect all the Mithril Bricks. (Single Player Only)
Achieve True Adventurer in every level. (Single Player Only)
Turn an enemy into a skeleton and make them dance.
Travel to Trollshaws as Bilbo.
Travel to Isengard as every playable Hobbit.
Use the Ent Draught on Pippin.
Defeat Gollum as Gollum.
Defeat an Oliphaunt as Legolas.
During 'Prologue', jump into the fires of Mount Doom as Isildur.
Craft the Fire and Ice Bows. (Single Player Only)
Finish one of Gimli's opponents as Legolas in 'Helm's Deep'.
Equip Aragorn with the Mushroom Crown.
Defeat 42 Uruk-hai as Legolas.
Fish perfectly 20 times by pressing the icon as it flashes.
Throw Gimli 30 times.
Complete 2 cooking puzzles.
Complete the Bonus Level.
Complete 'Mount Doom'.
Complete 'The Black Gate'.
Unlock all the Map Stones in Middle-earth. (Single Player Only)
Complete 'The Battle of Pelennor Fields'.
Complete 'The Paths of the Dead'.
Walk into Mordor.
Complete 'Cirith Ungol'.
Complete 'The Secret Stairs'.
Complete 'Osgiliath'.
Complete 'Helm's Deep'.
Complete 'Track Hobbits'.
Complete 'Warg Attack'.
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'.