The items required to win are :

The Map
Time ring
Third house key
Beginner's grimoire
Desert bird feather
Pogo stick
Heart plug
Advanced grimoire
Magical sponge
Shell Powder
Magical red shark fin
Black magic grimoire
Magical green shark fin
Magical purple shark fin
Heart pendant
Desert fortress key
Unicorn Horn
Xinopherydon claw
Pitchfork
Talking candy
The P stone
The L stone
The A stone
The Y stone
Health Potion
Turtle Potion
Anti-gravity Potion
Berserk Potion
Cloning Potion
P Potion
X Potion
The giant Spoon of Doom
Scythe
Summoning Tribal Spear
Monkey Wizard Staff (enchanted)
Troll's Bludgeon
Wooden Sword
Iron Axe
Polished Silver Sword
Pink enchanted gloves
Red enchanted gloves
Leather Boots
Boots of Introspection
Lightweight Body Armor
Enchanted Knight Body Armor
Octopus King's Crown with Jaspers
Octopus King's Crown with Obsidian
Candy Merchant's Hat
Rocket Boots

I don't put the Sorceress' Hat in the list because it costs 1 billion candies and it seems too long to reach for a speedrun.

I think we should add a category of speedrun on "Candy Box 2": All items, all weapons and all armor (Consumed objects count).
Without opening the candy box.