besides the chests will i get any rewards for hard since i ran normal this week?
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You will get some rewards for completing the traverse the abyss section, the crossing the bridge and killing the ogres section, and killing crota... If you picked up the two chests on normal you will not get anything from them on hard and deathsinger works like an exotic chest so same thing with her... If you beat deathsinger on normal than you get nothing for beating her on hard