I had similar problems with Patient Zero, even though I wasn't part of any group before starting the mission. I used a lvl 54 Vanguard tank with Elara Dorne as my companion. My gear wasn't that great (mostly orange with some purple mods) . In order to beat PZ, I had to (1) Activate "Heroic Moment" right before the fight (for some reason I couldn't seem to activate it in the middle of it), (2) Hit him with my legacy attacks right at the very start, and (3) Use an Aim stim in order to increase my damage. His heals are innate, and there doesn't seem to be any way to interrupt them. Interrupting his attacks is probably helpful, though in my experience it wasn't critical. Even with a tank spec, my healer companion, and increased damage output from the stim and my legacy attacks, it was still by far the most difficult fight during the Arcanum mission. The end boss was a piece of cake compared to PZ.