To make the minikits in Harry Potter: Years 1-4 visible, you need get the number of wizard hats listed below. To view them, go to the Room of Requirement above the shop and interact with the question-mark statue:
A Fluffy Encounter: 80 Wizard Hats
A Letter from Hogwarts: 10 Wizard Hats
Battle With The Basilisk: 140 Wizard Hats
Buckbeak Takes Flight: 190 Wizard Hats
De-gnoming The Burrow: 110 Wizard Hats
Defending Sirius: 180 Wizard Hats
Grindylow Attack!: 210 Wizard Hats
Gringotts' Vault No. 687: 20 Wizard Hats
Harry and the Hungarian Horntail: 200 Wizard Hats Required
Harry Versus The Dark Lord: 220 Wizard Hats
Harry's First Wand: 30 Wizard Hats
Lockhart's Magical Mistake: 100 Wizard Hats
Lord Voldemort Attacks!: 70 Wizard Hats
Peeves Causing Chaos: 120 Wizard Hats
Sneaking Around Hogwarts: 60 Wizard Hats
Snowy Battle in Hogsmeade: 160 Wizard Hats
Taming A Hippogriff:150 Wizard Hats
The Dueling Club: 90 Wizard Hats
The Flying Car: 130 Wizard Hats
The Mountain Troll: 50 Wizard Hats
The Stolen Remembral: 40 Wizard Hats
The Werewolf Gives Chase: 170 Wizard Hats