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