0) When you reach the last stand, try to have some (if not all) of the following:
- A crew teleporter with 2 mantis or rock crew
- One defence drone, and (optional) an anti-ship drone (beam is best)
- Cloaking (level 3 is best, but only level 1 is needed for most of the battle)
- Enough weaponry to reliably take down 4 layers of shields and deal some damage besides. (Don't rely entirely on missiles, phase 2 has a defence drone.)
1) The moment the battle starts, it'll cloak. When it uncloaks, use boarders to take out the triple rocket launcher, then the triple ion, then the beam. Leave the laser alone, the guy manning it MUST survive. If all the crew die, the ship will be controlled by an AI which passively repairs all the systems.
2) Once most of its weapons are down, try to kill off the crew in the main part of the ship. Fire at the medbay to destroy it, then send in the boarders. When they are on low health, teleport them back, heal up, damage the medbay again if it's been repaired, and repeat. Watch out for cloaking, though; you can't teleport out from under a cloak.
3) Once most of the crew are dead, bring all your guys back and take out the (almost defenceless) ship. If you didn't kill off all the crew in the main section, focus your fire on the cloak room. They'll rush to repair it, and when the ship breaks up, they'll be killed. On to stage 2.
4) This is the hardest stage. The moment the battle starts, send your boarders over to take out the rockets again, and activate a defence drone. It will shoot down most (if not all) of the boarding drones they send your way. If a drone makes it past and breaks in, focus your weapons on the drone control - even one point of damage will deactivate the boarding drone.
5) When you get a power surge warning, put exactly one bar into your cloaking system, but don't cloak until the drones are just about to shoot. A level-1 cloak will dodge the vast majority of the drones, and it will sync up with the next power surge.
6) Once the missiles (and beam, if you want) are down, take down the ship again.
7) This is it, you're almost there. First off, activate any anti-ship drones you may have and power your cloak to max, but don't cloak until the first volley of missiles is fired. The moment the super shield goes down, deactivate your drone and teleport boarders into the missiles for the final time. From there it's fairly straightforward, just remember that a level-1 cloak syncs well with the power-surge superweapon.
8) Annnd you're done. Good work.