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