Badge of Vows 99 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 99 is located in the Ancient Quarry near the southern most gate switch. Acquiring this one can be a bit tricky, because you have to destroy the wall (shown in the picture) to even see it. To do this, you'll need to be the Warrior vocation and use a heavy hitting ability: such as Arc of Might. This will cause the wall to crumble, and in some cases, knock the badge loose immediately. If the badge is still stuck in the ceiling, you will need to switch to a vocation that has access to a bow. Using the Mystic Knight Stone Forest ability may also dislodge the badge.
Note: It is recommended that you (or your pawn) have the Radiance augment skill to light up the area.