To those interested, I have timed when Crota moves from side to side. From the time the shield walls go down and you are able to start firing, you have 1 minute and 30 seconds before he rotates. That's the amount of time you have to clear out both sides, get the sword, and attack Crota. Once he rotates the first time, you have approx. 50 seconds until he moves again each time after the first rotation. This should help you establish a pattern. Good luck!