man, you're fighting a guerilla war. think of it as russia versus afghanistan; ak47 versus gunship...
you cant actually go head to head with them with the pea shooters you start with. so get ready properly as you have quite a few turns before they even come looking for you:
1. you start with 20 000 credits so you have the option to fully develope your worlds.
2. colonise fast, but do not become the front line let your allies take point. if you have to, colonise those front line worlds and give them to your allies.
3. on planets you want to keep, you need to be able to build quckly and research fast so plenty of factories and research buildings. don't worry too much about finance as you'll be selling tech and ships as they become obsolete.
4. keep your allies alive by supporting them with your own fleets, but if the worst happens and the front line falls then retake the world, hopefully get tech, give back to allies. repeat as desired.
5. occasionally a battleship or escort ship finds its way around the front line, so its good to have fleets on standby on your core worlds.
6. play on at least challenging/tough because all the DL ever do is churn out ships, and you need effective allies so give em a chance to help you.
7: eventually you'll get to the point where you are stronger than the DL and then go and kick their asses.
its not easy, but its not that hard to beat them either. i've yet to redo the campaign with v1.1, hope its harder than the last time...
later and good luck, init