LEVEL 15 is probably my favorite level. This is long. Read this whole reply if you want my full strategy. First there is:
-----SLOW EASY METHOD
*Hang around in the battleship for a while. kill all enemies that come near. first, make a few cruisers, then make lots of gunships. You'll need about 15 ships more than the 3 you started with.
*After you have about 15 ships in good repair, hyper over to the base, leaving about 3 ships behind for defense. Switch over to the Heavy Destroyer if you want. Build an Assault Transport.
*Make sure you have destroyed the station's defenses. Capture the station, and when the carriers come, use fullerenes+missiles against them (this is definitely the hardest part). If the destroyer gets destroyed, switch back to the battleship. if that one's already gone, restart the level.
*Once you've captured the station, guard it no matter what happens. Remember: any transports trying to get through will die, so don't worry about your planet.
*Build lots of gunships and cruisers, when you get about 15-20 again, hyper to the planet and go on a rampage. Babysit it and capture.
HOWEVER, THAT METHOD TAKES FOREVER, MEANING LOWER POINTS.
-----FAST HARDER METHOD (PREFERRED)
*Immediately switch to the Heavy Destroyer. Timing is everything. Quickly build a Gunship, and select the station as your target so it will go there when it's built. When it's halfway done, tell the carrier to go to the station.
*Wait a moment, then tell the battleship to go to the station.
*When the gunship is done, quickly build an Assault Transport. send it to the station.
*Now hyper over to the station. Its defenses should be almost gone by now. Remember, once the assault trans is done, start building gunships as fast as possible. Don't get a single scratch until you start fighting the carriers, and save every last one of your fullerenes. Don't let your assault transport die!
*When the carriers come, this is the hard part (again.) Use fullerenes and missiles. Try as hard as you can to stay alive, the destroyer is the best ship to destroy carriers in. Concentrate on the carriers.
*Once they're gone, build a few more gunships (be sure not to let them get your station, kill any of their assault transports) and go get the planet. Forget about your own planet; as long as the station's well defended no transports can get through.
*Destroy the planet's defenses, babysit it, build a transport or two, land, that's it.
Whew! that was long. sorry.
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Joolzman5 sez: Oh fudgemonkeys.