I happen to have very good luck with the Kestrel A (and about as much luck with the Engi ship, but that's a different story). Anyways, this time around... by the time I got to the final boss, I had FOUR Burst Laser MkII's, full reactor power, and at least one Defense MkI drone (the other was either another Defense MkI or a System Repair drone). I never dipped down below 75 percent hull.
In a similar success story (with the Kestrel A), I was on an achievement run trying to get 6 different crew members on-board my Kestrel ship... not only did I get that achievement (thus granting me the Kestrel B), but I also got the Crystal ship in the process. It was only my second time getting that quest and my second week having the game that I managed to get the Crystal ship. I also ended up winning that round.
I hear it's next to impossible to get the Crystal ship, yet somehow I managed to get it fairly early on.
