I think I may have had a revelation yesterday. There is a real depth of strategy to the battles I had not considered. Some of these brutal fights are not meant to be fought traditionally.
I built my fleet to have a long range of fire, powerful and plentiful weapons, and to engage in evasive strategies. Basically I would up my defense, haul ass out of my enemy's firing range, charge my attack gauge to max, then move up until my guns were in range, and release a barrage when the enemy let down their D.
Rinse. Repeat.
For average foes this should be successful. However, I realized that a boss that kicked my ass all of PAX basically is built for the same strategy. Only, his ship is many times better than my fleet.
The answer was disgustingly simple. If all of my primary weapons had a minimum range (get too close to the enemy and they cannot be fired) so must his.
I started the battle by engaging my defense (which stays in place until I attack) and closed on him. He kept backing up to get his primary weapons the minimum distance, and I used mt carrier's fighters to pin him down until we were ship to ship.
From that point we traded secondary fire, that does next to no damage. After a long firefight his huge health let him steal the win. I needed more firepower at close range.
I went through my fleet configuration and remembered a destroyer I got a long time ago, and had summarily mothballed after I got my second battleship. Its class is called a "Missile Destroyer" and it sports two missile launchers. I had shelved it because it required me get in close, whereas my battleships let me issue death from a long range.
I took out my less armored battleship and replaced it with the almost unarmored destroyer. I put my heavily armored flagship in front to absorb any damage we took closing in. If I lost the flagship I lose, but without the destroyer this plan would fail anyway.
I ran at him, using the fighters to hold him in place. The missile destroyer did its job; after a long fight I took him down.
The whole battle system has opened up to me since then.