The bounty objective is "Defeat opponents in the Iron Banner. Earn bonus progress by landing final blows on opponents with a higher Power level."
I would keep track of how many kills I get (not assists, just kills) and check progress during respawn, and it would not update progress correctly. I had lowered my gear level to 1555 so to possibly get the bonus progress.
I used my super and got 4 kills, and the bar progressed by only 1%. I got a kill with a shotgun and it progressed 2%. I got 2 melee kills and it did not progress. I got a triple kill by using my auto rifle, then my shotgun, then my grenade and it progressed by only 1%. I killed a player and it progressed by 1%, then later we killed each other at the same time with my kill coming second, and it did not progress at all.
These numbers make no sense and the bounty seems to be bugged and not tracking kills and progress correctly.