Each stage in Normal Mode has a number of hidden acorns; collect all of them in a stage to unlock an accessory. Beating each boss in Normal Mode for the first time will award you with an accessory. Clearing each stage in Mirror Mode for the first time will also give an accessory.

Unlockable	How to unlock
3D Glasses	Collect all acorns in World 8 boss
Afro	Collect all acorns in World 7 stage 1
Angel Costume	Clear World 4 boss in Mirror Mode
Antenna	Beat the World 8 boss
Big Pot	Clear World 2 stage 2 in Mirror Mode
Bird's Nest	Beat the World 4 boss
Blue Bucket	Clear World 4 stage 1 in Mirror Mode
Blue Ribbon	Clear World 3 stage 2 in Mirror Mode
Cake	Clear World 6 boss in Mirror Mode
Carrot	Clear World 1 boss in Mirror Mode
Chef's Hat	Beat the World 6 boss
Cool Unit	Collect all acorns in World 8 stage 2
Crown	Clear World 7 boss in Mirror Mode
Cute Sunglasses	Collect all acorns in World 4 boss
Deluxe Mask	Clear World 8 boss in Mirror Mode
Devil Horns	Clear World 5 boss in Mirror Mode
Drill	Clear World 7 stage 2 in Mirror Mode
Eye Mask	Collect all acorns in World 7 boss
Faucet	Collect all acorns in World 3 stage 1
Feelers	Clear World 8 stage 1 in Mirror Mode
Fish Costume	Beat the World 3 boss
Flowers	Clear World 2 boss in Mirror Mode
Glasses	Collect all acorns in World 1 boss
Green Ribbon	Clear World 4 stage 2 in Mirror Mode
Green Sunglasses	Collect all acorns in World 3 boss
Headphones	Collect all acorns in World 3 stage 2
Helmet	Beat the World 7 boss
Hibiscus	Collect all acorns in World 4 stage 1
Ice Cream Cone	Collect all acorns in World 6 stage 1
Laced Hair Band	Collect all acorns in World 6 stage 2
Mask	Collect all acorns in World 5 boss
Medium Pot	Clear World 2 stage 1 in Mirror Mode
Mohawk	Collect all acorns in World 2 stage 1
Mushroom	Collect all acorns in World 1 stage 2
Native Headdress	Collect all acorns in World 2 boss
Orange Ribbon	Clear World 1 stage 2 in Mirror Mode
Palm Tree	Collect all acorns in World 4 stage 2
Party Hat	Collect all acorns in World 6 boss
Plug	Collect all acorns in World 8 stage 1
Plunger	Clear World 3 stage 1 in Mirror Mode
Ponytail	Collect all acorns in World 1 stage 1
Rafflesia	Collect all acorns in World 2 stage 2
Red and White Hat	Clear World 7 stage 1 in Mirror Mode
Red Ribbon	Clear World 5 stage 2 in Mirror Mode
Santa's Hat	Collect all acorns in World 5 stage 1
Seed Leaf	Beat the World 1 boss
Silk Hat	Beat the World 5 boss
Skull	Beat the World 2 boss
Soft-Serve Ice Cream	Clear World 6 stage 1 in Mirror Mode
Stars	Clear World 8 stage 2 in Mirror Mode
Three-Scoops	Clear World 6 stage 2 in Mirror Mode
Tiara	Collect all acorns in World 7 stage 2
Toilet Paper	Clear World 1 stage 1 in Mirror Mode
Umbrella	Clear World 5 stage 1 in Mirror Mode
Watering Can	Clear World 3 boss in Mirror Mode
Witch's Hat	Collect all acorns in World 5 stage 2