The damage I was doing was actually fine. I was playing safe and consistently getting three hits and getting four in once if the timing was perfect. I think I only died once to a Crota sword swing if he went down.
My problem was taking too much damage or dying getting to the rocks after grabbing the sword. Thralls would slap me, crota would shoot me, or my health was such that a boomer would get me on the way back in. Any tips? Up my agility? Perhaps I'm jumping down too early to take down the swordbearer? More grenades from the team?
If your team is taking the swordbearer down quickly, there is no need to rush to the sword and put yourself in harm's way for any longer than necessary. That said, I usually rocket the swordbearer from the middle, so you should be able to manage without getting hit if you focus on strafing more than dps on the swordbearer. One small thing I've noticed is that approaching from around the pillars (nearest Crota) seems to help me avoid Crota's shots. It adds a couple seconds to getting the sword, but that shouldn't matter.
All that said, there is one great way to reduce the danger that requires nothing else on your part. If your team employs a bubble distract strategy, have the titan leave to put the bubble up when the swordbearer is at half health or so. As soon as the bubble is up, that will draw Crota's fire. Assuming the team has no problem taking down the swordbearer, you'll lose nothing and get the benefit of not getting hit by Crota on approach.
As for the thrall, I never, ever shoot. Even if there are a ton of them, I just grab the sword and use the fact that it has a large pickup radius to my advantage. The team can help by either throwing grenades or just sniping any cursed thrall. If you roll with the same people, you can designate those roles to make it easier.
And finally, if you do get hit, you should be able to manage assuming the boomers are taken care of. I have been at extremely low health when getting to Crota (typically when the swordbearer doesn't comply and I run down to rocket him) during successful clears. I don't know where you go to escape after a rotation, but I found that leaving the titan in the bubble for a few extra seconds while escaping helps. I tell the titan to leave when I am just running up the steps. The titan will get in just after me, and if the boomers touch anyone, it will be the titan who has a blessing of light active, not me. I also drop the sword as soon as I am off the platform as the delay when dropping it can cause me to get hit or lose my sprint. That helps me get to safety even when one hit would do me in.
Hope something in there helps.
