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 a level in co-op.
Collect more than 10,000,000,000 studs. (Single Player Only)
Complete 'The Mines of Moria' in under 15 minutes.
Travel to Isengard as every playable Hobbit.
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)
Fish perfectly 20 times by pressing the icon as it flashes.
Equip Aragorn with the Mushroom Crown.
Turn an enemy into a skeleton and make them dance.
Craft the Fire and Ice Bows. (Single Player Only)
Travel to Trollshaws as Bilbo.
Use the Ent Draught on Pippin.
Achieve True Adventurer in every level. (Single Player Only)
Defeat Gollum as Gollum.
Throw Gimli 30 times.
Defeat 42 Uruk-hai as Legolas.
Reach the top of Amon Hen without being caught once by Boromir. (Single Player Only)
Complete the Bonus Level.
Complete 2 cooking puzzles.
Unlock all the Map Stones in Middle-earth. (Single Player Only)
Dress a character completely in treasure items.
During 'Prologue', jump into the fires of Mount Doom as Isildur.
Complete 'Mount Doom'.
Complete 'The Black Gate'.
Complete 'The Battle of Pelennor Fields'.
Defeat an Oliphaunt as Legolas.
Walk into Mordor.
Complete 'Cirith Ungol'.
Complete 'The Paths of the Dead'.
Complete 'The Secret Stairs'.
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'.
Complete 'The Mines of Moria'.
Complete 'The Pass of Caradhras'.
Form The Fellowship of the Ring.
Complete 'Weathertop'.
Complete 'The Black Rider'.
Complete 'Prologue'.