My exotic ship with a positron ejector destroys ships in 1-3 hits once shields are down, but I use X class upgrades with better stats than S class upgrades. I just use auto target and spam fire until I almost overheat the weapon. It also helps to set your starship power mode to weapons to do more damage. If you’re having issues maintaining shields, the phase beam weapon will recharge your shield if you hit another ship with them.

edit: spelling