:UPDATE:
Just realized how old this post is and so here's the updated strategy from playing Admiral difficulty.
Okay, so bad news first. You have 3 more factions besides the NR that you have to worry about. The Greater Maldrood and the NR will be your early competitors and they will continue to attack your two territories. With the nerf to TIE Defenders (Not sure how bad it is, but in my playthrough I just haven't used them at all), they won't be as effective as they were in the past when you could build 10 squadrons and curb stomp most fleets you fight against. Also, if you lose your capital, your economy is going to take a HUGE hit. So you need to rush to get into the Deep Core.
The good news though, is that it's not really a huge rush to get into the deep core. Your primary objective will be Odik II. Capture it, and you will be rewarded with the SSD Knight Hammer. Also by taking Hakassi, you will also get Pellaeon. He will be fighting against you with the GM, but if you do manage to kill him he will still join with your forces after you capture Hakassi. Next good news. You don't have to fight through EVERY SINGLE PLANET to get to Odik II. Once you take Hakassi, you then capture the Tsoss Beacon and you're within striking distance of Odik II. If any of the other factions capture Odik II before you do, you will not lose the Knight Hammer or the hero Cronus. So again it's not a huge rush. Lastly, the AI for the IR factions will not huddle and camp around their space stations like they did before. They will spread themselves more and openly head out to attack you. Use this info to lure them away from targets of opportunities like an enemy hero and send the rest of your fleet to ambush.
Okay, so first things first:
You start off with Kessel and The Maw. One little change up they did was allow ground vehicles to be built at the Maw Installation. You will have access to light and medium vehicle factories from the start. Build up some ground forces like TIE Crawlers to support your small force of stormtroopers and other light units. Once done, unite your fleet and take over Bimmisaari. This will give you breathing room to build more units. At this point you will probably start getting attacked by the GM and the NR. Try to hold them back while you strengthen your numbers in the fleet. Before sending your fleets to attack, make sure to send in some probots to get an idea of what you're heading into. You have very few numbers of ships and not much of an economy to rebuild any losses you've taken. Once you have a strong enough force, head for Hakassi and capture it. Once it's yours, build Hakassi into a fortress world. Build a HVG, barracks, and all factories that you can. Hakassi will now be your "locked" back door as you move further into the Deep Core. By this time you probably have lost Kessel, The Maw, and possibly Bimmisaari. If not, try to build at least one of these planets into a fortress world as well just so you can keep your economy and more importantly, your unit cap up. Also, if you have lost these planets, than your capital is also gone and the huge economy bonus you would get from that. Don't worry too much if you do. Leaving behind any ships to hold these planets would be a waste and it's not your objective to hold these planets. Also, you can rebuild your capital on another world if you do lose it.
After taking the Tssos Beacon, head for Odik II and take it over. Again, make sure you're gaining intel from your probots before moving in. Squaring off against a death stack at this point of the campaign would be crippling. Once you take over Odik II you will be rewarded with the Knight Hammer and another hero, Cronus. This is where things get tricky, tiring, and frustrating at times as well. Hopefully the NR or the GM have been too busy fighting each other to send over a death stack at you, however they will send in small fleets of about 4-7 ships of mostly frigate types or smaller. Nothing too huge, but enough to destroy level one space stations that could open a way for an invading force. YOU CANNOT LOSE ANY MORE PLANETS! This is extremely important because with the lose of your capital from your starting worlds you will be losing credits possibly from your unit upkeeps. So you pretty much have to juggle building up your fleet and ground forces, building up your economy, taking over the rest of the Deep Core, and also defending your territory from raiding fleets from the GM and NR. With the Knight Hammer in your fleet, you can curb stomp pretty much whatever you have to attack so it won't be too hard, but the sheer number of attacks and having to rebuild your space stations over and over again will chip away at your economy and your sanity at times. To lessen the number of planets they can attack, make sure to hold Hakassi and if you have the time and the ships, head North to Pakrik Minor and turn it into a fortress world with 2 HVG's to support the level 1 space station there. Easiest and fastest way to take over the rest of the Deep Core is to send your fleet in, crush whatever they have there, than move back to either Odik II or Hakassi while leaving one ship that can provide bombing runs and bombardments for your ground forces. Rinse and repeat until the Deep Core is yours and all those planets to rebuild your economy.
If you have made it this far, still have the Knight Hammer, still have Pellaeon and Cronus, have taken over the Deep Core, and have stabilized your defenses, then congratulations. You pretty much have won this GC. It will take a long time to take over the rest of the galaxy, but at this point it would be incredibly bad luck to lose at this point. Hope this helps and add onto this if you have an easier method for any of the steps I've mentioned. Good luck Commanders.