I am able to confirm, in order to get the emblem for your specific subclass, you not only have to finish your subclass specific PvE quests, but ALSO PvP quests (killing Guardians with Meele, Grenades and then special) I was able to finish my set of Striker related PvP quests today (still not done with the create 7 orbs 3 times in a strike though in PvE) and it unlocked the striker emblem. After I finished the Striker PvP quests, it started a new chain of quests for Defender related PvP quests. So, in order to get the subclass emblem, you HAVE to finish the PvP quests that ask you to do specific kills with a specific ability. The only problem is, you can't start the PvP quests with the subclass you want to unlock the emblem for, it starts with a preset subclass by default and you won't get the PvP quests for any other subclass until you finished that one. After the Striker PvP quests, it unlocked the Defender PvP quests for me, without me doing anything, so I assume if you want to get the Sunbreaker emblem for example, you have to finish Striker AND Defender first, to even unlock the quest chain.