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