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The Eye of Sorrow harnesses the power of the Sea of Black Tears to launch black liquid that coats enemies, dealing damage. Once the Hammer of Infinite Fate DLC is installed, it becomes available after completing "Pilgrimage of Screams". There is no cost for the upgrade.
Use of the Eye of Sorrow is required to unlock the following achievement/trophy:
Kill 20 Drowning Doom units with the Eye of Sorrow.