I'm sure I'm not the first to post this but felt I needed to share it anyway. I used this strat last night with a LFG group that didn't have a comfortable sword carrier. After a couple of wipes trying to do it the old fashioned way, a guy chimed in and taught us this "new" strat. Completed the challenge almost immediately (the sword glitched on the first attempt) I know it's a little late to try it this week but it's definitely worth giving it a shot, if not just for practice.
Here's a link to a Reddit page that provides a walk through and video. Have at it!
https://www.reddit.com/r/DestinyTheGame/comments/637k1h/struggling_with_crota_cm_try_this_strategy/?st=J26W52QK&sh=686dd2d1
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I have used this strategy it works well however I prefer the normal strat. The only strat I hate and will not do is the one where someone places a bubble near the people bringing down crotas shield to block Boomer shots instead of killing boomers. If a group is adamant about doing that strat I give it a few attempts and if we can't even get a damage phase on him without someone dying I leave.