I have been to the location marked on the map to contain stingwings and have killed them all. They never drop a stingwing barb when killed. Am I doing something wrong?
I think you might just be hitting some bad luck. The barbs are not a regular drop but they are not rare either. You should find they drop every 2 or 3 enemies at worst. You will just have to keep killing them. There is nothing special you need to do to make them drop a barb.