Here is the full list of all 37 LEGO Harry Potter: Years 1-4 trophies - there are 20 bronze, 12 silver, 4 gold and 1 platinum.
Collect all the bronze, silver and gold trophies
Defeat 10 enemies with a Muggle character
Defeat 20 enemies with Fang
Complete the Quidditch level within five minutes
Defeat Harry (as Voldemort), in the Graveyard
Defeat Quirrell in the Quirrell boss fight, using Voldemort
Defeat the mountain troll, using Quirrell
Complete the game to 100%
Buy every version of Voldemort (Quirrell/Tom Riddle/Voldemort)
Collect all of the Gold Bricks
Hide in a barrel as Snape
Buy the entire Gryffindor Quidditch team from Book One
Collect all of the Red Bricks
Rescue all students in peril
Use the Time-Turner
Collect all of the house crests in Year 1
Collect all of the house crests in Year 4
Get True Wizard in every level
Unlock all Animagi
Collect all of the house crests in Year 3
Buy the entire Weasley family
Collect all of the house crests in Year 2
Defeat 20 spiders with Ron
Destroy 50 Devil's Snare plants
Scare 20 students using a ghost character
Collect 10 million studs in one level
Freeze 20 characters using Glacius
Complete the Story Levels in all four years
Complete Year Four Story Levels
Complete All Story Lessons
Turn the sound and music down to 0 in the options menu whilst in the library
Complete Year Three Story Levels
Complete Year Two Story Levels
Collect 500 ghost studs
Complete all the LEGO Builder tutorial levels.
Complete Year One Story Levels
Knock over ten characters using a ride-able object