You must first complete the game once to unlock Time Attack mode. To begin a challenge, walk up to a statue in the temple and pray (circle).

Unlockable	How to unlock
Cloak of Deception	Defeat 14 Colossi in Time Attack mode.
Cloak of Force	Defeat 4 Colossi in Time Attack mode.
Flash Arrow/Brown Agro	Defeat all Colossi in Time Attack mode.
Fruit Tree Map	Defeat 10 Colossi in Time Attack mode.
Lizard Detection Stone	Defeat 8 Colossi in Time Attack mode.
Mask of Power	Defeat 12 Colossi in Time Attack mode.
Mask of Strength	Defeat 6 Colossi in Time Attack mode.
Whistling Arrow	Defeat 2 Colossi in Time Attack mode.