When you collect special item crates in the following levels and then beat the level the item will become unlocked.

Unlock Astronaut Hat:
Collect the special item crate in level 1-1 and then beat the level.

Unlock R.I.P. Gravestone:
Collect the special item crate in level 1-2 and then beat the level.

Unlock Creepy Speech-Bank:
Collect the special item crate in level 1-3 and then beat the level.

Unlock Insignia Flag:
Collect the special item crate in level 1-4 and then beat the level.

Unlock Eyeball Hat:
Collect the special item crate in level 1-5 and then beat the level.

Unlock Alien Hat:
Collect the special item crate in level 2-1 and then beat the level.

Unlock Post Gravestone:
Collect the special item crate in level 2-2 and then beat the level.

Unlock Captain Speech-Bank:
Collect the special item crate in level 2-3 and then beat the level.

Unlock Strong Worm Flag:
Collect the special item crate in level 2-4 and then beat the level.

Unlock Logical Speech-Bank:
Collect the special item crate in level 2-5 and then beat the level.

Unlock Helmet Hat:
Collect the special item crate in level 3-1 and then beat the level.

Unlock Obelisk Gravestone:
Collect the special item crate in level 3-2 and then beat the level.

Unlock Doctor Speech-Bank:
Collect the special item crate in level 3-3 and then beat the level.

Unlock Meteor Flag:
Collect the special item crate in level 3-4 and then beat the level.

Unlock Zap Flag:
Collect the special item crate in level 3-5 and then beat the level.

Unlock Padded Hat:
Collect the special item crate in level 4-1 and then beat the level.

Unlock Digital Gravestone:
Collect the special item crate in level 4-2 and then beat the level.

Unlock Babe Speech-Bank:
Collect the special item crate in level 4-3 and then beat the level.

Unlock Crush Flag:
Collect the special item crate in level 4-4 and then beat the level.

Unlock Petrified Gravestone:
Collect the special item crate in level 4-5 and then beat the level.

Unlock Red Hat:
Collect the special item crate in level 5-1 and then beat the level.

Unlock Slab Gravestone:
Collect the special item crate in level 5-2 and then beat the level.

Unlock Female Computer Speech-Bank:
Collect the special item crate in level 5-3 and then beat the level.

Unlock Tentacle Flag:
Collect the special item crate in level 5-4 and then beat the level.

Unlock Visor Hat:
Collect the special item crate in level 5-6 and then beat the level.

Unlock Yellow Hat:
Collect the special item crate in level 6-1 and then beat the level.

Unlock Cross Gravestone:
Collect the special item crate in level 6-2 and then beat the level.

Unlock Princess Speech-Bank:
Collect the special item crate in level 6-3 and then beat the level.

Unlock Bolt Flag:
Collect the special item crate in level 6-4 and then beat the level.

Unlock Column Gravestone:
Collect the special item crate in level 6-5 and then beat the level.