I was using the Federation Destroyer: http://www.ftlgame.com/forum/viewtopic.php?f=11&t=17194
I had:
Full shields
Dual laser 1
Dual laser 1
Auto 1
Burst Scatter 1
I had a really lucky game the entire time but I had made it to the boss without finding any good weapons. But it was really easy killing the first stage of the boss:

But then, the second stage I was wrecked in. but as I died I was like "NOOOOOO" so I jumped away from the fight with a yellow hull, but it still said 'GAME OVER'


Thanks everyone for reading!
-TSR