These items can be acquired through the Hard Time Attack Mode. You receive one item for every two Colossi you defeat in Hard Time Attack Mode.

Unlockable	How to unlock
Cloth of Desperation ("Parachute")	Defeat 14 Colossi in Hard Time Attack Mode.
Fruit Tree Map	Defeat 6 Colossi in Hard Time Attack Mode.
Harpoon of Thunder (Long range projectile weapon)	Defeat 2 Colossi in Hard Time Attack Mode.
Lizard Detection Stone	Defeat 10 Colossi in Hard Time Attack Mode.
Queen's Sword (From ICO)	Defeat 16 Colossi in Hard Time Attack Mode.
Shaman's Cloak (Decreases damage taken)	Defeat 8 Colossi in Hard Time Attack Mode.
Shaman's Mask (Decrease damage taken)	Defeat 12 Colossi in Hard Time Attack Mode.
Sword of the Sun (Reflects light even when in the dark)	Defeat 4 Colossi in Hard Time Attack Mode.