Okay, I beat it with this.

Septum Class Destroyer
Price: 1,000,000 Credits
Aftermath

Honestly, if the AI targeting was better, I would most likely (though not guaranteed) have taken less damage. My ship kept targeting weird parts of the ship that really weren't a threat, allowing yours to blow up several modules.
EDIT: The largest improvement that you're gonna want to go for is compartmentalization. More defense, including shields and flak or at least PD would be good, it seems like your design would be heavily vulnerable to missiles.
The firepower is also rather low, for a 1 million + ship, I think. I'd rate it somewhere between a 3 or 4.
EDIT 2: Also, I assumed laser beam spam meant ion beams, not normal lasers. Not that I really have any ion beam based ships.
EDIT 3: Did another battle for fun, took less damage this time.
