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