You can play this mission with either the Imperial Guard or the Eldar. You can switch sides anytime you want until one of the factions either wins or fails. Trying to support one faction with the other is pretty useless so just pick one and ignore the other.
Imperial Guard
Your goal is to escort the Ultramarines' Land Raider from the bottom to the top and through the Psychic Shield. You can't control the Land Raider directly, but you can call it to your Command Squad (Sturnn to be specific) within a limited range. You need to use this ability to call it through the last gate. On the way you will be harassed by massive amounts of Chaos Space Marines and Orks spawning from the bottom edge. You can only build Listening Posts and Plasma Generators, but there are some structures you can commandeer to raise your Squad/Vehicle Cap.
There are basically two ways to do this: you can either dash for the top or hole up in your little base, defend against the waves there and prepare. When you move for the Psychic Shield, you can either let the Land Raider take its own path or open shortcut gates by capturing Strategic Points.
If you decide to strike for the Psychic Gate right away, let the Land Raider go where it wants and support it with whatever infantry and vehicles you can scrape together. If you open the shortcuts, you need to divide your troops and the enemy will just follow you through. Don't try to assault the huge Disorder base at the bottom, you will die. The Ultramarines get replaced with drop pods if they die (the reinforcements seem infinite, but they will actually run out at some point if you get into a really epic fight) so just keep an Engineer along to repair the Land Raider. Commandeer the the small Imperial Guard base next to where you start with your Command Squad, build a Listening Post and some Plasma Generators and start research/production there while directing all you can to protect the Land Raider. Don't worry about the base, the enemy will attack your commander and the transport. Take your Command Squad north to commandeer an Infantry Command (a bit to the right from your base), a Mechanized Command (higher up near the left edge) and a Mars Pattern Command (near the upper edge, left from a Critical Point). Send one Guardsmen Squad along to capture the Relic near the Critical Point so you can build a Baneblade. Now run back and slow down the enemy waves with whatever works for you.
If you want to hole up for preparations and maybe some revenge, commandeer the starting base and keep the Land Raider around your Listening Post (by calling it with your Command Squad whenever it wants to leave) and support it with what it takes to blast the enemy waves. Start research/production and run your Command Squad up to commandeer the other structures again (you can dash up to the Mars Pattern Commmand and be back before the Land Raider decides to leave). Build the Baneblade and bring it down to your other troops. Now you can have maybe 4–5 squads of Karskins, Command Squad, the Land Raider and Ultramarines, five Leman Russ tanks and the Baneblade kick the crap out of Disorder. Take care, though – even with the buildings gone there will be lots of Disorder troops spawning from the bottom edge.
When you get the Land Raider through (remember, you need to use the Command Squad) you win and the Eldar get wasted. You now get the Titan of the Emperor final mission.
Eldar
With the Eldar, you must move your Webway Assembly to the other side of the Psychic Gate. This means backstabbing the Imperial Guard, destroying their Thermal Plasma Generators to open the Gate, moving a Bonesinger through, building a Webway Gate on the other side and using the Relocate ability.
You start at the corner, safe for the moment so start teching but move on eventually, because you're very close to a rather large Ork base and you don't have much space to build. Taldeer tells you to move your base and then to scout the Psychic Gate entrance so just do what she says. When you approach the place you should move to, the Imperial Guard get pissed and turn hostile. Basically you just kill some Imperials, set up your base, take a Ranger Squad and some firepower up north along the right edge to scout/destroy and slip a Bonesinger through (teleport from maximum range once the way is open). Relocate one structure. Not much more to it.
You will be attacked by Imperials coming from the top and Orks from the bottom. From the Imperials you'll see lots of Guardsmen Squads and the occasional vehicle (no Leman Russ tanks, luckily) and you should also be prepared to blast the Infantry Commands they go hide in. Use Warp Spiders and Fire Dragons when you move up (be sure to get Fleet of Foot). The Orks come with their basic infantry setup and vehicles (mostly Wartraks) so the same works for defense. The Guardsmen have a long range so a Dark Reaper Squad or two may be useful. For vehicles, go for Fire Prisms or Wraithlords. Use your Seer Council where you need it most and save the Farseer for defense so you can hit Eldritch Storm if overwhelmed.
When you move the Webway Assembly, the mission is won and the Imperial Guard is stuck outside their own barrier. You now get the Ancestral Powers final mission.