Badge of Vows 96 is a quest item from the From A Different Sky - Part 10 DLC. Merely picking it up satisfies the goal needed to complete the quest.
Badge of Vows #96 is located south of the Tomb of the Unknown Traveler in the Verda Woodlands. It sits atop a spire that can only be reached by using Levitate. You will need to make a running jump and delay your levitation for a second in order to have enough airtime to reach the column.