"Complete a daily Heroic story mission with at least one Black Armory weapon equipped."
(Heroic) Postmodern Prometheus completed x3. First without any BA equipment; my fault. Second with Rnging Nail; no go. Third time with Ringing Nail, Hammerhead, and forge legendary chest, arms, legs, and class armors (I figured "at least one?" couldn't Hurt to put on as much as I've got). Still no completion. So frustrated. hmu
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That's an adventure, not a story mission. You need to load an heroic story mission from the Vanguard menu.