I recently won the game for my second time, despite a bit of bad luck at the start (a single missile killed 2 of my crew while they were healing in my medbay)
I ended up winning with the engi cruiser, manned by only 2 engi, with 2 iron blast II weapons, a pike beam, an anti-ship drone, and a defence II drone. No cloak, 4 shields, only a couple bars of energy available for the engines, and fully upgraded doors (which made one of the engis beat out a mantis for the most kills) I was able to ion spam the boss so hard that it didn't even drop me below 50% health despite my lack of defences. I also unlocked the rock-cruiser during this run.
~Edit~
I had planned to open up FTL and take a picture of my stats screen to show the engi with most kills (along with the mantis with most piloted evasions), but the print screen button seems to take nothing but a picture of the loading screen long after I have finished loading.