Oh sweet jesus this one was fuuuuun.
Spoilers in case you don't want to know my little solution to this headache.
Don't feel bad man; this was the first mission I wiped on. Felt bad.
I advise that you work on dodging as much fire as you can while focusing on the most threatening targets. Don't use your 10 second Electronic Warfare Pod at the start or you'll miss it later on the mission (the part right after you first pass the capital ship... you know the part I mean).
Also, your EMP blast should be used as you see fit, but I personally like to use it while attacking the capital ship. It should make short work of the ships turrets and will let your shields recharge a little faster providing you don't shoot.
One of the big things I notice that helps a lot is that you should switch your Power Conversion Module to regen shields faster every chance you get, whether it be a lull in combat or if you only have to shoot down 1-2 targets (use missiles as your lasers will make your shield charge more slowly).
Other than that, the fighter's do more damage collectively than just the advanced enemy ship, so you can focus that last.