Hi!
It sounds like you’ve got plenty of upgrades, but make sure you have upgraded the health of the structures as this will make your structures last far longer against battleships.
Also, make sure you have enough energy regeneration so that all of your guns can fire.
As for strategy in the level it sounds like you need to spend more on mining early on. Use the quiet time at the start of the level to really mine as much as you can, remember the enemies come from the same places each time so you can learn which asteroids are safe at the start.
Laser turrets need to be upgraded to maximum to reach battleships effectively, use a combination of these and railguns.
I hope that helps! 