I present here a guide to defeating the boss ship, almost guaranteed, almost every time.
To show that this isn't pure theorycrafting, here is my highscores page:

Yes, I have a terrible win/game ratio. I could make excuses like "Sector 1 restarts! Abortive achievement runs!" but it is what it is so judge me as you will.
Minimum requirements:
- max shields, and near-max engines
- 20 power bars (more is better)
- teleporter, with boarding party. You will want at least 2, and mantis or at least crystal/rock are very preferable.
- anti-missile drone
- any laser weapon (i.e., does hull damage, does not cost ammo)
Total minimum scrap cost, assuming you start with a level 1 shield and no weapons or extra systems:
330 shields + 345 engines + 75 teleporter + 80 drone control + 50 anti-missile drone + 355 power bars (to 20, starting with 8) + laser weapon 50 = 1285 (a regular normal run will acquire 2-2.5k, sometimes more)
Optional requirements:
- any missile/bomb weapon
- multiple anti-missile drones, or a level 2 drone
- boarding drone
- teleporter level 3
While this may seem like a lot of requirements, if you play a typical normal run, you should pick it up fairly easily.
This is most probably the easiest way to beat the boss from what I've seen, and since I switched to this strategy I have killed it every run where I had the needed stuff.
And so, without further ado, the strategy:
When the boss fight starts you should have the following online:
- all of your shields and engines (16 bars)
- teleporter to the highest level you have (1 bar)
- anti-missile drone (2 bars)
- oxygen (1 bar)
This ONLY needs 20 power bars! (22 with max teleport)
1. launch your anti-missile drone
2. beam your boarders into their missile control and kill it until it is dead.
2a. if you have emp bomb, drop it on the missile control. if you have other bombs/missiles, aim for ion or laser weapon control
3. once missiles are dead, return your boarders and proceed to take out ion then beam-laser control. DO NOT kill the operator in the pulse-laser room!!
4. once the 3 weapons are incapacitated, i.e. the ship can only shoot 3-pulse laser at you, you may power down engines, and power down shields to only 3 pips, as needed to power other weapons and/or boarding drones. prioritise missile/bomb weapons.
5. start killing off their boss ship's crew. this will be easily done if you can disable/destroy their medbay, especially if you can add a hull breach in there. if you can't, warp in 2 waves (or a full 4-pad teleport) of boarders into a room on the side (e.g. cloak) and start hammering the crew. they only have a 2 slot medbay and aren't terribly bright. some of them will die eventually. when they do, work your way over to shield control and disable that, so that you can hit the medbay with lasers if needed.
again, this is a SLOW method which requires a lot of patience! however, the end result should be:
TL;DR at the end of stage 1 you want to have achieved:
- no crew alive in the boss ship EXCEPT ONE in the pulse laser control. DO NOT KILL HIM. it is super important that he is there, as this will prevent the ai from turning on and auto-repairing everything.
- for stage 2, your anti-missile drone will shoot down the ai's boarding drones; the rest is easy, disable missiles then shields using your boarding party, and plink away at the hull with your laser weapon.
Enjoy your successful boss runs!