I didn't even have any starship building skills when I finished that mission and my ship tore through everything like paper. I had the best possible A class (the lowest level stuff without skills) equipment you can buy at New Atlantis, and 4 particle cannons for massive DPS. Barely took damage and was obliterating the ships in 2 or 3 shots and the cannons themselves took just a few more. I'd suggest just going and doing some minimal upgrades.

Or to cheese: make your ship a square frame so the enemies just shoot the middle and never actually hit you cuz there's nothing in the middle.