Well The biggest thing that I like about this game is Deathstars. To be able to build them and support them how ever is a tricky matter. They are resource hogs. which should not be built unless you have an ample surplus of maintenance points. I usually wait until I have at least 2000 open points, and at least one large shipyard. Usually a Ten or More Adv. Shipyard facility can build a deathstar in under three hundred turns.
     One of the things that needs to be done first though is to fill up the ship yard with ample fighters. At least fifty to initially stock the star. Then at least a hundred more for all the ships in the supporting fleet. I dont like to field a Death star with less than a 150 fighter squadrons in the task force. Theres nothing like going into orbit around an alliance world with a hundred or more fighters planet side and more in a fleet.
    Although I havent tried this against the computer, but If you come accross a planet with a heavy fighter defense, try to take a neighboring planet then deploy the fleet a day ahead of the death star. This will allow your fleet to soften the defenses before the Star arrives.
     This can be a problem if the fleet gets in trouble against the opposing fleet and fighters. If this happens try to retreat the fleet to the next planet. When the Death Star reaches the planet. Immediately target the gun on one of the opposing fleets ships, take the shot then sound the retreat. The star by itself can retreat before the fighters destroy it. This can be a slow meand sof wiping out a large fleet if you have built a deathstar shiled on the other planet. the opponent might chase it down and get caught on the other side of a shield.