EDIT: Also, I was playing on easy due to not beating the boss before.
During my most recent session of FTL, I decided I'd try the Zoltan type B again, just to see how playing with it went. Christening it the Asimov, I began my journey. Once I had enough scrap to upgrade my shields (the 100 scrap needed for the first upgrade seems a bit high to me), everything went swimmingly. However, through all of my trips to stores and random events I was never able to pick up another weapon - I was really hoping to get missiles to use against the flagship, but I could never find one. The only weapon I ever picked up was another Pike Beam, which I promptly sold to help upgrade my ship. I found myself jumping into sector 8 with full shields and slight upgrades to every other system, the engine having the most points after the shields.
Despite my reservations that I was severely under-equipped, I jumped to sector 8 anyway. I was lucky enough to dodge a lot of hits from rebel fighters with my 40% dodge change before jumping away from most conflicts, and I went into the first stage of the flagship with almost full hull health. To my surprise, the two Ion Blasts and the Pike Beam served very well in getting the shields down quickly and allowing for a small opening before cloaking to use the beam in, doing pretty good damage to the hull and moderate damage to systems. I kicked butt in the first stage - although the flagship had 1 hull point left at one point and it took me three minutes to get that point down - and quickly sent my crew over to destroy the flagship's weapons in stage two. Through careful managing of my crew and systems, I survived the boarding drones (even when they sent drones to the cockpit - that wasn't fun) and, to my surprise, beat the second stage without too much trouble.
I had about 75% hull at this point, still in the green, and I decided to make a few jumps to a repair point and then to stage three. I also upgraded my engines with my remaining scrap. I had one flagship jump left to spare by the time I got to the ship, and was only missing one hull point. I repeated my strategy of autofiring the Ion Blasts at the most critical systems and maximizing damage with the hull beam, and my two Rockmen and Mantis on board served to deter the boarders. It was smooth cruising after I got the missiles and most of the crew down, and to my great surprise and happiness I managed to defeat the flagship soundly.
I don't know if the Zoltan type B weapons just happen to be the best for the flagship or if I got lucky, but my first victory ever feels like a great achievement to me.
Proof is in the pictures:
Both pictures are also links, just in case the size of the first one messes things up.

