Badge of Vows 14 is a quest item from the From A Different Sky - Part 2 DLC. Merely picking it up satisfies the goal needed to complete the quest.
This is probably the trickiest of all (sub)quests in the line of quests of 'From A Different Sky' so far. In order to obtain this Badge of Vows, read this instruction guide carefully!
NOTE: There is more than one way to get this badge
First of all, you are in need of Curatives that restore some good deal of Health, for instance Harspud Juice or Potent Greenwarish, since you need to fall and hurt yourself in order to get to this Badge of Vows, unless the Arisen is skilled well enough in the use of the Core Skill Levitate, because it's situated near the base of the waterfall between Cursewood and Deos Hills.
Before attempting the fall onto the ledge on which the badge is to be found, make sure (when facing the waterfall's edge) to stand to the very right near the waterfall's edge, against the cliff to your right, and look for a stone next to the falling water on which you can let yourself fall a few feet without hurting yourself. You probably may find the red circle on the minimap useful as a guiding spot. Now that you've let yourself fall those few feet onto that stone, be VERY careful not to walk to your left (towards the falling water), since the Arisen may instantly fall down all the way without using the animation preventing a fall first! Best you can do now to prevent failure at all is by saving your game before making the attempt to reach the ledge below.
If looking down, you should be able to spot the glowing Badge of Vows and if night has fallen use a Lantern to spot it. Once you've seen the badge, you should be able to coordinate your fall down onto the ledge. Although it doesn't look like a ledge at all, the Arisen will fall near the badge and hurt himself / herself, losing an estimated 500 Health points. Pick up the badge and congratulations on obtaining it! But... You've yet to get away from this location and there are two ways to do so: either use a Ferrystone or consume some Curatives for the final fall to the waterfall's base (losing an estimated 400 Health points) and drown to get washed up ashore a little to the north of your current location. A (wet) job well done!
Follow the riverbed's edge East (to your right if coming from The Abbey) Jump on the rocks (stay as close to the right as you can).
Save when you reach the rock (see pic. A). Slowly inch your way to the edge. DO NOT jump or you will most likely end up in the water with the Brine and have to try again. Once you have the badge the only way to get down is going into the water and letting the Brine take you. Don't worry. You will still have your badge and completed the quest.