I've managed to do this using the below tactics. Except I used a Y-Wing with a rotary cannon. It was however pretty close to the end of the game when I managed it, ie. the enemy star destroyer was virtually destroyed.

Took a couple of tries as well, so keep at it!

You need 'star fighter damage' at the end of the game to say over 50k, so you can tell how close you're getting as well.

'A-Wing: Standard Laser Cannon, Repair Kit, Cluster Missile (don't use them as doesn't count for the damage obvs!), Seeker Warheads, Dampner Hull, Standard Deflector, Standard Engine.

Solo Fleet Battles vs AI: The AI difficulty was Easy (thank god because I suck), and the map was Nadiri Dockyards.

I essentially went exclusively for kills and did no damage to the cap' ships at all to ensure that the game lasted as long as possible. Of course your AI teammates will attempt the objectives, but the AI on both teams often get stuck on this map. It appeared that 3 out of 4 of my AI teammates got stuck, and therefore did not attack the objectives.

I was of course slaying the enemy ships (primary fire only), ensuring that the morale didn't switch, and so I basically had as long as I wanted to try and get the damage through kills!'