This week quest steps to complete has kill 50 champs in Expedition Salis of Shipsstealer Step 35 of 62, but the problem of gameplay is champions dont show upbecause "Hyper" guardians are so good in game and throwing engrams, Bungie may be spawn more champs or higher up difficulty levels so atleast we see champs to complete this task, that should take 5 runs rather than more than 50 runs just to complete one step of quest.
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Do legend Lost sector's or hero NFs. Its like 17 champions.
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It doesn't have to be Champions killed in Expedition. Champions in any activity counts, and those in Master Ketchcrash give more percentage. There are around 10 in this week's Nightfall on Heroic, so you could just run 5 Nightfalls and get it done.