Funny you are asking this today

, because I just succeed in doing that.
After watching zzandrio second attempt at a no shield run I tried to do the same. Now the very sad thing is that I didn't record my success

. Before starting the game I was like "this is my first attempt, no need to record, I must first train how to play properly with the stealth ship..." and here it is, I did it and it was my second victory in normal with the stealth ship A (I don't like those ships so I don't play them

).
Also I did nothing what you guys are suggesting ; but I was very lucky and you need that.
At the end my ship had:
-----------------------------
6 bars in engines (not enough to have 100% dodge, I had like 98% )
7 in weapons ( 1 pike beam, 1 burst laser III, 1 ion bomb)
6 in drones (1 anti ship II, 1 anti ship I)
0 in shields
1 in O2
1 in medbay
1 in teleport
3 in cloak
enough energy to power everything except the medbay and the teleport
-----------------------------
2 in pilot
2 in sensors
3 in doors
-----------------------------
6 crew members
1 mantis
1 rock
4 humans
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1 long ranged scanners (because asteroids fields are gg)
1 weapon pre igniter (previously it had 1 scrap recovery arm)
1 stealth weapons
At the start I aimed a lot at the fights beacons to get a lot of scraps. I was lucky for the most part with the encounters, I had to flee 2 battles in the 2-3 first sectors, one was near a sun with boarding mantis.
It went so well My first repair at a shop was at sector 5 (I unlocked the corresponding achievement), take into account that I still had repair encounters (but not a lot, maybe 1 or 2).
The first thing I augmented was the cloak at level 2 then the weapons to 3 bars (it's cheap and prevent very bad situations) then doors to level 2 because I had very few crew members.
Very early I had a shop with a scrap recovery arm and a stealth weapon (it also had some systems like shields and drone and teleport), of course I bought that asap. I then augmented the cloak to max.
But I had no luck in finding weapons, I bought a ion bomb but even with that It was getting hard in the mid level sectors (3-4-5). I had no choice but to buy a burst laser III. The problem is that the cool-down is very slow and it misses a lot (had to flee one guy because of too many misses in 2 attempts!, and It was only a lvl 3 shield) oh, and I almost forgot, it costs a lot to power up (it costs a lot in scraps too) .
The stealth weapons helped A LOT, I took very few damages and could upgrade the weapons and buy some good stuff. The next system I bought was the teleport but I used it only twice during fights and I don't think I had a blue event with it. During all that time I had only 4 in engines, so I upraded it a bit after that.
The last system was the drone control with an anti missile one. Later I bought an anti ship in case my offensive power was not enough. Finally I bought an anti ship mark II because of the zzandrio video, to beat the boss.
The pike beam came very late in sector 7, the weapon pre igniter at the start of sector 7 or end sector 6.
With all that the run was very easy (at least for someone knowing the game well enough, still had to flee sometimes). I didnt get a lot of scraps during the run but I did not have to waste it on repairs, on the other hand I had to buy a lot of things. In the end I had just enough to run my systems and power my offensive threats.
the boss:
phase I was a walk in the park, ion bomb on the shields, 2 attack drones (mark I an II), then laser III on the shields and pike beam from the stealth room to the shields then across the ship starting with the beam room to the heavy laser. Cloak was used to dodge the missiles. Phase I was cleared with 1 hull damage.
phase 2 was living hell, same tactic as phase I, bomb on the shield then laser 3 on the shield then pike beam across the weapons. Cloak was used at start, still cloak level 3, just before the beam drone attack. missed some Ion bombs
I couldn't kill it before the power surge, and the cloak don't last enough if you use it at the start of the battle like I did. I had to survive long enough for my drones to take the shield down before I could pike beam him to hell.
I survived the power surge with 11 hull left, weapons where on fire and down to 2, sensors and doors went down. the engines and cockpit had like 1 damage each. Luckily the drones where good till the end.A few seconds later and I was dead, maybe I should have cloaked later and focus on the beam+drone room with the pike beam.
There was a repair beacon nearby, but 3 jumps were not enough to go there and go back to the mother ship.
phase 3 was harder than expected. The shield lasted a long time, ion bomb missed, too much misses. Cloak was used for the missiles, I let the heavy laser hit me because I was too hesitant. The cloak ended just before the power surge hit me...I evade most of it but I was also targeted by 3 missiles before I took the ship down, 2 of them hit me. I was barely alive, one more volley and I was dead.
Conclusion:
The lack of a 4th weapon slot is deadly against the boss, the firepower with attacks drones and the weapons is barely enough to survive long enough. The stealth weapon is a must have, it makes the run easier and prevent a lot of damage from the last boss, stealth should be kept on level 3. Weapons pre igniter buy some time, maybe it's the little thing that makes you win the game instead of dying.
I was very lucky to get the ideal augments for the stealth ship: pre igniter and stealth weapons.
I still don't know what's the best weapon combo, ion bomb is just overpowered and makes you win the game in a normal playthrough. A beam lets you do guaranteed hits, but you have to go past the shields and it's hard with just 3 slots. Maybe the ion bomb + laser III was very good after all, maybe a halberd beam would have been better than the pike beam.
Still, phase 3 is hard enough if you cannot repair yourself. Surviving phase 2 is not enough, but it's the hardest phase for sure.
session stats:
Ship defeated 30
Beacons explored 89
Scrap collected 1528
Crew hired 6
Final score 3772