The way I win (and I usually do win on easy) is to make sure that I have a full crew and then I use the teleporter to send my boys and girls in sets of 2 over to the enemy ships weapon compartments. Here's the trick - you can easily kill the guy who's manning the weapon and disable the weapon because the compartment is completely cut off from the rest of the ship - no help is coming. When you fight the ship the 2nd and 3rd times, the weapons are unmanned and more easily destroyed. I take out the rocket launcher first, then the laser, then the beam, then the ion.
While I'm destroying the weapons, I turn off my own weapons and crank up shields, engines, teleporter, stealth (1 point only) and any drones and other defensive systems. Once the flagship's weapons are offline, I power down my teleporter and any other system I don't need and go crazy with the weapons.
From there, it depends on what weapons I have available. If I've got lasers out the ass, I just sit there shooting at his shields. If I have bombs, I nail his shields again and then fire lasers or beams at various areas (especially the stealth module in phase 1) to get the crew running around like madmen.
One VERY important thing - do NOT kill all of the enemy crew. If you do, then the ship's AI takes over and will repair the 4 main weapons. Bad news.
Best equipment - drones, teleporter, stealth, 1 bomb, multi-shot lasers. Upgrade shields early and often to avoid having to spend money on repairs. You're going to need the shields anyway, so better to upgrade them now rather than later.
Oh, and the first time I beat it was with the regular ship and a bunch of lasers. I didn't figure out all the above tricks until I had more runs under my belt.
