Almost had The Best Run Ever.
Started as the Torus (named the USS Redshirt). In the very first sector I scored a Mantis to add to the crew, and found an enemy ship that would never be able to do damage unless I intentionally lowered my shields. So what did I do? I grinded.
All four crew members, experts in all four stations. I also discovered that a single Ion Blast II could keep a life support room more or less permanently offline, allowing me to suffocate and take whole many a vessel.
It didn't all go my way, though. I missed out on two opportunities to unlock a new ship. The first time was on a trip through the Mantis homeworlds. I had checked the wiki, I had bought a crew teleporter and advanced medical bay and had plenty of practice at killing crews with my boarding party. Never got the special event. Then in Sector 7, which was the Engi homeworlds, I managed to get the intel required for the final part of the Stealth Cruiser quest. Sadly, the rebel fleet was right on my tale and I missed out for good.
Easiest fight ever this time. Four shields, Defense Drone II, and maxed-out Cloaking covered me on the defensive side. Weapons were the Ion Blast II, Heavy Laser I, and Small Bomb, as well as two Anti-Ship I drones. In all three stages, I first used the boarding party to eliminate the flagship's weapons, before dropping some of my defenses to attack.
First phase went swimmingly. Second phase was defeated with no damage thanks to a constant small bomb barrage on the flagship's drone control, which eliminated it's defensive drones, it's normal attack drones (did nothing to stop the special DroneSpam attack, but with four shields that was a non-issue), and most importantly the boarding drone, so I didn't have my crew constantly fighting off killer robots and patching holes in the hull. Once the weapons were silenced and the enemy drone control was destroyed and on fire, second phase was all but won.
Third phase was the only one to deal damage, because I couldn't silence the enemy weapons quickly enough. First I had to bring down the special shield, and then I had to fight off several boarding parties. The Defense II drone helped, but there was a little too much incoming fire, especially from HeavyLaserSpam. Still, flagship eventually went down, only taking about 7 hull points off.
Ironically, not a single crew member of the USS Redshirt died. The boarding party had a couple of close calls, but in the end everyone got home safely.