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