Beat the game and save your game at the end of the credits. You can now enter Time Attack Mode by pressing the Circle Button to pray in front of a Colossus statue. By beating the Colossus under the required time limit in Time Attack mode, you can unlock new weapons and items. Read below for the rewards, in the order that you'll receive them.

Whistling Arrow - Distracts a Colossus when you fire it.
Cloak of Force - Increases the amount of damage your sword will do to a Colossus.
Mask of Strength - Allows you to inflict deeper wounds into a Colossus.
Lizard Detection Stone - Allows you to find the white tailed lizards throughout the land.
Fruit Tree Map - Allows you to find the Fruit Trees around the map more easily.
Mask of Power - Allows you to inflict more grievous wounds on a Colossus.
Cloak of Deception - Makes you invisible to the Colossus.
Flash Arrow - Explodes and can damage a Colossus without hitting its vitals.

Hard Time Attack Mode unlocks more options and this version of Time Attack is unlocked after clearing the Story Mode on Hard difficulty.

Harpoon of Thunder - A new Colossus-whacking weapon.
Sword Of The Sun - Allows the light beacon to operate even in patches of shadow.
Fruit Tree Map - Identical to the cheat earned in Normal Time Attack.
Shaman Cloak - Hero's defenses increased and he takes less damage.
Lizard Detection Stone - Identical to the cheat unlocked in Normal Time Attack.
Shaman Mask - Increases the hero's defence. This cheat's effects stacks with the Shaman's Cloak. Think Red Ring from Legend of Zelda.
Cloth of Desperation - Hand-made parachute allows for soft landings. Similar to the gliding ability in Sly Cooper.
Queen's Sword - An ICO easter egg. It has the side benefit of killing a Colossus with great ease, but without the nuclear fallout.