Oh man, I did all levels up to this one first time. Then had to try about 6 times to get this.
Firstly things NOT to do:
Fight the dreadlords.
Worry about reclaiming lost planets.
Help your allies.
Things TO do, this is what finally won it for me. There may be better ideas, it was quite close:
Quick-build everything you can.
Have full industrial spending all the time.
Have a high percentage on reasearch, as that is the only one you can't buy.
Build a starbase on the Economic resources you start next to, upgrading with mining modules if you want, but NO weaponry.
Rush left with your constructors and colony ships, your goal is to expand your range as close to the objective world as possibel.
If you need to use starbases to get there, you SHOULD upgrade these with weapons. The dreadlords will still destroy them, but if you get the shield defence module the Yor and Drengin ships that attack it will mostly die.
Design a scanner drone, a Cargo hull kitted out with sensors, it can reveal a huge chunk of space, and avoid most threats.
Now then, as for technologies, this is what I found I needed:
One or two support techs, but that was only because I couldn't quite reach without.
Planetery Invasion, and the upgrades if you want them.
Moderate strength beam weapons (plasma 2 or Phasers 1 I think I reached).
Medium Hulls.
Logistics, enough to let you have three medium ships (15?).
As good sheilds as possible.
The strategy I used was to build up as far as possible until the dreadlords came along. At which point get a fleet or two of war ships and some troop transports.
Using the large LOS revealed by the scanner drones, manoeuvre them along the bottom of the map (beneath the Arceans) then up passing by the right hand side of the Drengin and Yor. If you get attacked by patrols you should win. But best save your strength for the attack on the objective.
Hopefully this image may make things clearer:

Good luck!