You need to complete 24 story levels in Years 1-4 to unlock the trophy:
Year 1:
The Magic Begins
Out of the Dungeon
A Jinxed Broom
The Restricted Section
The Forbidden Forest
Face of the Enemy
Year 2:
Floo Powder!
Dobby's Plan
Crabbe and Goyle
Tom Riddle's Diary
Follow the Spiders
The Basilisk
Year 3:
News From Azkaban
Hogsmeade
Mischief Managed
The Shrieking Shack
Dementor's Kiss
The Dark Tower
Year 4:
The Quidditch Cup
Dragons
The First Task
Secret of the Egg
The Black Lake
The Dark Lord Returns
After the 24th level is complete the trophy will unlock!