Defeating the boss with Engi ship type A & this setup

[Sovereighn2280]

Round 1: Replace the Beam Drone with your Hull Repair, use Rockets on shields and empty rooms. Use Ion on Shields. Use the laser to take out the weapons. (Power all Drones)
Round 2: Rockets on Shields and Empty Rooms. Use Ion on Shields. Use the laser to take out the weapons and the drone system. (Power all Drones)
Round 3: Same Idea as Round 1. But unless you have good shields and engines, your toast on this stage.

[UberFubarius]

Round 1: Replace the Beam Drone with your Hull Repair, use Rockets on shields and empty rooms. Use Ion on Shields. Use the laser to take out the weapons. (Power all Drones)
Round 2: Rockets on Shields and Empty Rooms. Use Ion on Shields. Use the laser to take out the weapons and the drone system. (Power all Drones)
Round 3: Same Idea as Round 1. But unless you have good shields and engines, your toast on this stage.

He already won the boss fight. But regarding hull repair, I suggest using it in between fights (if you have gotten to a point where you need hull repair in mid-fight... you're more than likely screwed).
Hull repair only repair 3~5 hulls per use (I think).

[GoldenShadowGS]

This is a fine loadout. Ion to keep the shields down, and halberd and attack drones to slice and dice the ship after the shields are down.