7 kills is for PvE not PvP. I was stuck on that part for a long time. I actually managed to get a 7 kill streak in crucible with it too but it never checked off on the quest line. At first I thought ok maybe I have to get 7 kills with no assists in between (managed that too) still no progress. Went into PvE killed 7 opponents and boom quest completed....well at least until the next reset. Wish bungie would clarify.