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)
During 'Prologue', jump into the fires of Mount Doom as Isildur.
Get 100%. (Single Player Only)
Collect all the Red Bricks. (Single Player Only)
Complete all the Fetch Quests in Middle-earth. (Single Player Only)
Craft every Mithril item. (Single Player Only)
Unlock all characters. (Single Player Only)
Defeat Gollum as Gollum.
Collect all the Mithril Bricks. (Single Player Only)
Craft the Fire and Ice Bows. (Single Player Only)
Use the Ent Draught on Pippin.
Achieve True Adventurer in every level. (Single Player Only)
Fish perfectly 20 times by pressing the icon as it flashes.
Turn an enemy into a skeleton and make them dance.
Unlock all the Map Stones in Middle-earth. (Single Player Only)
Walk into Mordor.
Complete the Bonus Level.
Dress a character completely in treasure items.
Throw Gimli 30 times.
Travel to Isengard as every playable Hobbit.
Travel to Trollshaws as Bilbo.
Complete 'Mount Doom'.
Complete 'The Black Gate'.
Complete 'Cirith Ungol'.
Complete 'The Battle of Pelennor Fields'.
Defeat an Oliphaunt as Legolas.
Complete 'The Paths of the Dead'.
Complete 'The Secret Stairs'.
Complete 'Osgiliath'.
Complete 'Helm's Deep'.
Finish one of Gimli's opponents as Legolas in 'Helm's Deep'.
Equip Aragorn with the Mushroom Crown.
Complete 'Warg Attack'.
Complete 'Track Hobbits'.
Complete 'The Dead Marshes'.
Complete 'Taming Gollum'.
Defeat 42 Uruk-hai as Legolas.
Complete 2 cooking puzzles.
Complete 'Amon Hen'.
Reach the top of Amon Hen without being caught once by Boromir. (Single Player Only)
Complete 'The Mines of Moria' in under 15 minutes.
Complete 'The Pass of Caradhras'.
Complete 'The Mines of Moria'.
Form The Fellowship of the Ring.
Complete 'Weathertop'.
Complete 'The Black Rider'.
Complete 'Prologue'.