Fight 1:
With riggers (and anybody with drones) watch for that boarding drone. They shoot out of the right side. Put up your defense drone if you see it or even if you think you missed it. I hate those things. I still would have brought out the defense drone just in case it shot it. But that's me, my hatred of boarding drones is probably a little irrational
You weren't perfectly safe, but pretty much. The drone and basic laser together could actually take down 3 shields and the beam could have periced one. It's not likely enough to worry about but it could happen.
You should have closed all the doors (to close the airlocks) and then opened all the doors (interoir only) and hten turned your oxygen up to 2. I don't agree that you shoudl have bought it, but you had it in an otherwise unlosable battle so you may as well have used it.
And you assuredly should have turned the defense drone on for the second boarding drone
I wouldn't even have considered boarding that ship. Some ships should just be destroyed. Boarding with Engi is... well it's a terrible choice
You did a good job runnign around to get your teleporter time to recharge though. Then... You sent them back in! 
TWICE!? GAAAAAAH10/10 for style, though. Holy cow that was tense.
Fight 2:
With the D-Drone out you're essentially safe.
You don't need to take your weapons offline to not shoot them. Just hit their number or select them and they'll become untargeted. Then, when you need them, they'll be ready to shoot.
This time I agree with you. They're softened up so there's less risk to teleport in. I also like your "Risk all or win nothing" strategy considering how much an underdog you are.
Fight 3:
Good job savign your guys with the ion bomb. Whew!
At least you realized you hadn't kept ioning their shields. Good choice bombing the doors. Had you ion bombed the shields you'd have lost your guys.
Boss 1:
You should have waited for hte ion bomb before shooting your burst laser. Though with their cloak their shields were coming up anyway. This first phase is tough on a weapons-only strategy because of that.
Your ion bomb should never leave the shields. 2 of those in a row and their shields are DOWN. If you can keep the cloak down (with the missile) you win the fight. And take a lot of their guys down too.
Every time a missile misses, it reaffirms my hatred of them.
You too no damage in that fight. Buy yourself a beer!
Video 2!
Boss 2:
I liked the teleporter strategy. Maximum use of resources.
You took your oxygen down but left your medbay up...
I tried to find more faults, but you realized all your mistakes during the battle and hey, no damage. You can't really argue with that, especially in the 2nd phase!
Boss 3:
Level 2 medbay doesn't help medibots. All you needed was level 1.
Your ion bomb was fully charged when you turned it off. You wasted the 500-second (or whatever it is) charge time by turning it off when all you needed to do was remove the targeting.
The whole battle would have been over much sooner if you'd just concentrated both ions on the shields until they were down, and then moved the ion 2 to the cockpit. Then you could just burst laser everything else starting with missiles. I'm not 100% sure but I think you'd have never taken any damage, or maybe just took 1.
But congrats! Well played, fought, and won!
Fantastic 20 minutes! The song to this run: 
