Just finished it with the Kestrel on Normal. Interestingly, it was a rather "unlucky" run where I stupidly lost two crew members to asphixiation (totally my fault), and spent a lot on repairs because of very strong ship combos (also, I fled more battles than in any other game so far).
As a result, I ended up without a teleporter (no point in it anyway, since I didn't have any rock or mantis), AND no drone system. Weapons weren't that hot either, a Fire Beam (which got no use at all during the boss battle), the starting Burst Laser 2, a Heavy Laser (one of the worst weapons in the game), and a Pegasus missile. I was curious to see whether the Pegasus would be enough to get through the flagship's defenses, especially stage 2. As it turns out, it was (by virtue of shooting two missiles). Since I never use missiles, I had 60+ for the final battle.
I simply priorized the flagship's triple missile launcher with the Pegasus each phase, then shields. Once the shields were down, the rest was relatively easy. Had my entire crew except the pilot running up and down the ship fighting the boarding drones all at once and fixing stuff, was quite funny. They manned their stations like 20% of the time.
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Got a repair node right before stage 3, which again was quite easier than 2, and it was smooth sailing from there. Final score: 4593, a whole lot better than my original Normal victory with the Kestrel.
Subset Games should really consider either switching stage 2 and 3's gimmicks around, or toning down stage 2, especially defense-wise. Stage 3 is pretty much a formality at this point.
