You CAN do it, but it'll take forever and requires cheese.
At the start, go out with missiles and do as much damage to it as possible. When you're down to the final base, switch to all shields, and as they take damage, pause, go to ship design, empty one of your shield slots, wait for the module to explode, rebuild the shield in that slot, then do the same thing with the next one once the first rebuilds (make sure to keep track of which shield you're replacing, or you'll lose your full one). If you do it right, you'll be able to keep at least 1 shield up at all times. If your shield gets really low, hug the base by repeatedly move ordering on it while you're waiting for your next shield to build. If you get alot of shadow charge, you can temporarily switch to missiles to get more damage on it.
That's how I beat it for the first time, I was in a similar situation to yours.