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 all the Mithril Bricks. (Single Player Only)
During 'Prologue', jump into the fires of Mount Doom as Isildur.
Collect more than 10,000,000,000 studs. (Single Player Only)
Travel to Isengard as every playable Hobbit.
Defeat Gollum as Gollum.
Travel to Trollshaws as Bilbo.
Complete 'The Mines of Moria' in under 15 minutes.
Complete all the Fetch Quests in Middle-earth. (Single Player Only)
Unlock all characters. (Single Player Only)
Get 100%. (Single Player Only)
Collect all the Red Bricks. (Single Player Only)
Craft every Mithril item. (Single Player Only)
Achieve True Adventurer in every level. (Single Player Only)
Walk into Mordor.
Turn an enemy into a skeleton and make them dance.
Complete the Bonus Level.
Fish perfectly 20 times by pressing the icon as it flashes.
Equip Aragorn with the Mushroom Crown.
Craft the Fire and Ice Bows. (Single Player Only)
Dress a character completely in treasure items.
Use the Ent Draught on Pippin.
Defeat 42 Uruk-hai as Legolas.
Throw Gimli 30 times.
Complete 2 cooking puzzles.
Unlock all the Map Stones in Middle-earth. (Single Player Only)
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'.
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'.
Complete a level in co-op.
Form The Fellowship of the Ring.
Complete 'Weathertop'.
Complete 'The Black Rider'.
Complete 'Prologue'.