So, The FTL RNG gods decided to prove a point on this.
Here's a screenshot (or two) of a Win/Flagship kill on Hard with Stealth A (The Nessario). I have the starting two weapons, and a Flak I, and a Combat Drone 1. That's it.
You may ask yourself, "Project Mercy, why would you use such terrible weapons?!?!" and I would answer "because that is the grand sum total of all damaging items to be had in this run." A shortage of green sectors, and a shortage of fuel to scout the ones I had (including having to fight off the rebel fleet at 0 fuel THREE TIMES. Yes AE, I really detest your inability to put weapons in shops.
Anyway:
Augments were a Scrap Recovery Arm and Long-Range Scanners (the titanium casing got vendored at the first store)
The point here being, you don't need some massive setup to win. Just some luck and some tactics. A cloak helps a ton too if you don't have a weapon advantage.