I'm still struggling all around, mostly because I need more training in using boarding correctly.
I had an insanely good ship going there, and then I lost two boarding crews shortly before facing the boss and that kind of killed me. In the end, I faced the boss with just 4 people and weak weapons because I relied on boarding all the way. I took out all his weapons with boarders, but then we just sat there and neither of us could harm the other. I couldn't get his shields down and I couldn't board his main section, either. Well, in the end I tried and lost all my people, just as I expected.
Dang, without that horrible loss I could've made it. I had 3 Mantis, 2 of them with very high melee skills. Fully upgraded teleporter and a human to fill out the 2nd boarding crew, so I could've sent in 2 crews and take him down.
Note to self: You absolutely need at least one bomb or missile against the boss so you can disable the medbay and/or shield room. Firebomb would probably work best.