I've beaten the main campaign on hard... (good luck with blasting the cannons off the Sathanas.)
Trebs trebs trebs if you can get them. Use the Ares once it's available (24 trebs capapcity). If you can't get trebs, go with Interceptors - you can carry a ton of them, they do a fair amount of damage, and you can track faster and more accurately than with hornets. Tornados, while fun, tend to have half a salvo miss, and take up a large amount of space considering you're firing 8 of them at a time.
The Morning Star is surprisingly useful. Doesn't do much damage, but knocking Maras out of their flight paths so you can nail them with a missile or two is good. The fast re-fire rate and long range is also helpful.
Speakling of which, I found lasers perferable to prom-rs... the refire rate on a prom-r is SLOW... lasers let you walk your fire towards them, for a greater chance of hitting.
Let your wingmates take the heat whenever possible. If you're the first in line against a wave of fighters, you *will* die. I spent a lot of missions flying far, far away from combat and then sniping enemies from relative safety.
Capital ships are your friends when you're engaging fighters. If you have a cap ship, draw the fighters towards it (have your wingmen defend the cap as well). You can use the cap to absorb missiles meant for you by just afterburning to another side of the ship. The cap's defenses (flak, anti-fighter beams) can also cut apart fighters on their own.
Enemy Caps: They all have areas where their guns *don't* cover. Try taking your time, approaching from underneath, the rear, somewhere away from the flak cannons if you can. Sending in a decoy wingman can also help, have him attack first, while the rest of the squad takes out annoying flak guns/weapons/engines/beam cannons.
Take on bombers whenever possible. Your wingmen will have a ton of trouble with them, and get themselves as damaged as if they were fighting fighters. You can probably take on entire waves of them yourself, trebs or no.
Don't be afraid to swap or steal a fighter from another group for yourself, or re-assign your squadmates to be better capable of fighting. If you only have to disable one subsystem of one ship, it isn't necessary for the entirety of Alpha Wing to have disrupters and stilleto IIs. In fact, you'll find a lot of time even having bombers is worthless, as the AI will screw up bombing runs a lot.
Hmm... lastly, you can run from people fairly well if you max your engines and just a-burn continuously. Also good for getting to and from escorts and mission objectives. Re-directing energy is important as you get less afterburner, shield and gun power at harder difficult settings.
Hope that helps a bit!