This video shows a generous preview of the Dust Palace,ps3\ps4 exclusive timed content.
At .1:35+following you can hear the speaker telling you that the bosses will have specifics weaknesses,in this case you can spot em just looking their capes,as himself hints.
Watch it :D
EDIT: In this Strike Mission you can get as loot,probably on the hardest difficulty,the 2 exotic weapons, Monte Carlo and Hawkmoon,accordingly exclusive contents for ps3\ps4,
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Every boss has to have a weakness or they'd all be indestructible. Just like the devil walker and that big ass eyeball