Here's a video of our squad killing Crota in about 4 minutes before spawning ogres. I used a hunter to be the sword bearer with full invisibility specs, and a titan came along with me to drop a shield. I jumped up from the center while invisible for the first run as fast as possible, and went to the rock on the right for the 2nd and 3rd runs,
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Awesome run dude! I notice most people just do RT, RT, RT but what I do is RB, RT, RT, RT. It gives you an extra 7000 damage on him and its easy to do as you run at him. You dropped his health to the T in crota with three drops and the way I do it I drop his health to about the same in two drops. I also do one super on the second drop but ya just a little advice to everyone out there. Your way works great but teams I'm with are never able to drop him three times before the sword goes away.