I have beaten him 5 or 6 times now, all on easy. General strategy is:
4 points in shields, duh.
a dodge around 40%. This takes 4 power to engines and having both the engine crew and pilot crew be maxed out in their skills (actually, that's about 37-39% I think?).
Some good, old fashioned luck.
Plenty of spare crew. You'll need the usual party of Rogers and Hammerstien men to run around and punch intruders and also provide back up repairing. Don't underestimate that last part. Racing to get systems back to health ASAP can really help.
There's nothing fancy about how you attack. You throw every single thing you have at him, try to overwhelm the shields, and then do damage. My preferred strategy is beam heavy, but I will use launchers depending on what I find along the way. Since he's got excellent dodge and 4 shields, you've got to alpha strike every time you hit him (that is, fire everything or nearly everything). Once you damage his shields enough that you can get to critical systems easily, you still need to periodically attack the shields because they'll get repaired.
Another good trick I learned is do not fire your weapons as soon as it comes up. Wait till you can fire all your weapons at once for the first barrage. This will help overwhelm the shields helping you bring them down and damage them. Once the shields are down feel free to fire at will.
Now, ideally I would have something like Blaster mark III (5 shots, 1 damage each, 4 power), blaster mark 2 (3x1, 2 power) and maybe a heavy laser (2x2, 2 power). Or a small bomb launcher (underrated, it does 2 system damage). But really any number of things can work. I think I just beat him with the Kestrel using a Blaster Mk II, Heavy Laser, Halberd Beam, and Small Bomb Launcher. Obviously a crew member with maxed weapons skill is really important. Barring an accident, you should have that no problem. If you have less than 6 points of active weapons, you are probably going to have a rougher time of it. I prefer to have 7 or 8.
I will say this, I believe I have observed that e.g. the Heavy Laster (shoots twice, 2 damage each) will only eat 2 shield points up if it hits both times. I always like to have a blaster in my arsenal, but fate won't always help there.
There are two augments that, other things equal, really help in this fight:
The "decrease weapon recharge time" augment. Nuff said. This is always the augment I hope to get first unless I'm going early cloaking.
The "when you warp in all weapons are charged". You might think this one won't matter as much but do not under-estimate it. It's a free volley to open the fight!
With the first augment and a great gunner you'll be attacking every 13-14s at most I think. From there, it's back to luck. If he rolls exceptionally well on dodges (and you don't), it can go south and there's nothing you can do about it. I've lost to him with a number of promising ships for this reason. Tip your cap and go have a drink.
Cloaking is really powerful for ships who can get it, e.g. the kestrel. My poor federation cruiser is no longer cloaking eligible, but I have beaten the last guy several times with cloaking + cloak weapons. For form 1, the weapon on the inner-right side of the boss ship (actually, this one is always there but see below) is a freaking Gatling missile launcher. It shoots 3 missiles and it's super scary. I prefer to cloak when this is fired (and hopefully he'll be shooting other stuff too). Ditto for form 2. Form 3 will be something you have to discover on your own. Obviously if you run cloaking stealth weapons is a huge priority. But the 100% dodge you get from cloaking is really useful in the fight, so not having stealth weapons is not the end of the world. If I have cloaking I always try to get it to 3 points, but I consider 2 the minimum. That can buy you a lot of time to repair systems or deal with borders.
Doors 3 is really useful starting on form 2 of this fight (and really useful in the last few sectors!). I usually save that upgrade for late though.
Andrzej Doyle is absolutely right that boarders can be really useful in this fight. It's important to keep in mind that there is no one path to victory. After the beta update that took away cloaking Fed cruisers, I managed a few more wins. Mostly beam-heavy stuff but I made great use of bombs in two cases (I love small bombs because they only eat up 1 power but do 2 damage). I had a mixed-arms game (using some boarders) go really well until I ran out of places to repair and then lost in the second form.
Targeting priorities:
Shields are first priority, obviously.
- Form 1 I like to go after the Gatling launcher next. Then it depends. Weapons or engines.
- Form 2 I go for the drone bay before the Gatling launcher usually. The ship will throw a lot of drones at you. This helps alleviate that.
- Form 3 Back to targeting weapons.
Lastly, it takes more luck. Sometimes you'll prepare to do this series of fights and have repair nodes/stores near by that you can use to stay fresh. Sometimes you won't. I have lost promising ships that way too - a node got swallowed while fighting the first or second form and I was too beat up to finish him. Them's the breaks.
It took me a number of tries to beat him, and it can get frustrating. Stick with it. You'll break through eventually.
Killing the crew in first phase means they won't be there in the next two, same if you kill them in second phase: they won't be there in the final, so killing them can be a good tactic as they may trouble you later.
If you kill them all you won't win that phase or overall, instead the ship will go into auto-pilot and will slowly repair all its systems much like the auto-assault scout drones in earlier sectors. It's best to leave one enemy crew alive, maybe the isolated guy on their laser tri-shot; because fighting an AI Boss is much harder than fighting a single panicky engineer.
When the ship flees to its next phase your boarding crew will be killed if they are still on board, same if you destroy it completely with your crew on board, meaning their noble sacrifice won't go down in the credits.
Best Answer
Assuming you don't have any viable counter-attack plan with your current setup, you might want to consider retreating.
In the advanced edition the flagship has to occupy the "base" for 3 consecutive turns before you lose. If you can visit a shop and trade a weapon for another that might do the trick. More likely there are some encounter beacons you haven't completed or allowed the rebels to capture. These will give scrap.
The best option, however, is reaching a repair station which in the advanced edition will give you scrap in addition to other benefits. If you truly will reach a deadlock, you'll need to use some extra scrap to change your loadout.
Oh, and the best part about retreating? They'll have to hack all over again, and they might choose your sensors next time!