You want help on completing the mission?
Well I have not played that mission (yet). But cracking open the map and senario files I can give you a general plan:
So, you start out in area 1 with a standard force of ships (survey, miner, colony, scout) and one special ship, the Anorian Battle Cruiser (going to be referred as the ABC). I assume it is a very powerful ship (It should be anyway). This is good because the Yor start out with a rather large amount of ships in areas 2-6. Closer inspections on the name suggest all of them have missiles and PD. Keep that in mind as you research your weapons and defenses of choice.
Starting off you have a basic load-out of technology except one thing crucial: Planetary Invasion. You are obviously going to need that in order to beat the Yor. In your first turn, start researching Xeno Economics. On your home planet, rush buy a recruitment center and start building only two factories. In your starport, rush build a Radar Station. If you do not have such a design, I suggest you to go to the ship yard and design one. It is basically a cargo hull with alot of sensors attached to it. This ship will help provide advance warning should the Yor attack. Once you get to the main space screen, set your survey and miner ships to auto and send your colony ship to the nearest planet next to your starting planet. Develop this planet by rush building a recruitment center and building at most two factories as well as a starport. Keep your ABC close since even though it is powerful, it is possible you could lose it and it will hurt your mission gravely.
In the next turn, your Radar Station should be done. Move the ABC and the Radar Station towards the location marked by the yellow X. Set the Radar Station to Guard mode once it arrives. That way, if it sees enemies, the screen will center onto the station and it should show you enemies. Keep your ABC close by to attack the enemies. Then, rush buy the starport on your second planet and also rush by a Small Hull Ship with weapons of your choice. After it is completed, send it to the ABC and form a fleet with the two of them.
Develop your planets and patiently wait until you build up a sizable attack force consisting of your ABC and more fighters. Send a few fleets to attack area 2 and eliminate all ships in the area. Assuming the Yor did not snatch up the planets there, send in a colony ship or two to claim and develop them. Station your fleets next to the Yor planet in area 2 and make sure no ship gets built there. Blow up the Yor Mining starbase in area 2 (if there is one) and also destroy the asteroid mining bases if the Yor has them.
Once you obtain Planetary Invasion, build a transport and send it to the Yor planet in area 2. they should fall. After that, keep on playing and you will eventually win. I made a suggested route for you to take when attacking but the way you go about the mission is up to you.
On the note on abilities, I suggest you max out economics mainly so you can develop your economy easier. Everything else if up to you but I would invest in better weapons ability to enhance the performance of the ABC.
Hope this helps!