I randomly found the Wormsinger rune, had it in my inventory for some time and then used it. Killed the champion that appeared and then some taken appeared just after, so I killed them too.
Found an Agonarch rune and it said to kill hidden taken threats to charge the rune so I ran around for a bit and found one that spawned, killed the hive major (with Hawkmoon) first and then the acolytes, and it didn't count towards the total.
Went somewhere else in the Dreadnaught and the same thing happened. I killed the hive major first and it still didn't count towards the total even though I killed all the taken enemies.
UPDATE:
Doesn't matter whether you kill the taken with legendary or exotic weapons, it is random as to whether or not you get the kills to count. Killing minions first or killing the hive major first makes no difference.
This quest is bugged and needs to be fixed.
UPDATE 2:
Stuck at 2/7, running around and killing taken but nothing is working.
[u]UPDATE 3[/u]:
I know what I'm doing now, it's not a bug so Bungie and players can disregard this post.
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You said hive for the first two then said taken so I think you have it at least figured out