The Amulet of Uroborus is an item that Kratos acquires at the very beginning of Chapter 13 - Passage to Delphi, after defeating Pollux & Castor. It allows him to heal and decay various objects in the game, essentially repairing them or deconstructing them to various points to proceed with the story.
In combat, the Amulet is used to hit an enemy and slow down time for it, allowing you to get free hits on that enemy. It is activated by holding L2 and pressing Square. You need 5,000 red orbs in order to power up this item to level 2, increasing its area of effect, as well as decreasing the cooldown time before being able to use it again.
