The winning build was, at the time of the Big Fight:
Redtail Kestrel layout
6 power in shields (3 dots)
6 power in engines
3 power in cloaking
4 power in drone control
Anti-Ship Drone II
Burst Laser I
Basic Laser
Basic Laser
Small Bomb
7 crew members
Sensors, Doors, Oxygen, Medbay weren't really relevant, but for the record Medbay and Sensors were each upgraded by one point.
I think the two biggest pieces here were the Cloaking and the Small Bomb, both of which were *critical* to the second round of the boss fight. Without cloaking you will have a hard time surviving...

This is awesome, thanks for sharing this.
I am thinking that doors and O2 upgrades might not be as useful as I think. I haven't nabbed a cloak yet, but since the cloak comes standard with the Kestral Layout 2 I think I need to work on getting that upgrade. I can live without the missile by default and frankly don't use it that much as is.
Actually, the cloak is not standard with Kestrel's Plan B Layout - I had to pick that up somewhere on the way.
Oh. Ok that makes sense, thanks!
Got my wife playing FTL as of this evening. On her third-ever jump she wound up in front of a too-close sun with her Oxygen and Doors on fire. We switched to my machine and paired for a sector after that, then she fired up her own game again. This game is brutal, I tell ya. :)
It really is. Not as brutal as some Roguelikes i've played though. Like I said in an earlier review of FTL, it dares to be fun.