This mission features a massive NOD base that must be breached in order to attack NOD's temple prime. To start, select all your units and attack-move them toward the northeast. Clear everything from the area to ensure your safety. Attacks from the NOD base will come (generally) in the form of infantry waves from the northwest and vehicle attacks from the east. Your first goal should be an expansion base, once you've unpacked your MCV.
The most tempting target is the tiberium patch to the east. Take a surveyor, along with the mammoth tanks and deploy there. Make the mammoth tanks guard the area, and deploy the rig you started with there to keep them repaired. Back at your base, build six APCs and another rig. Place them in the northwestern of your base, near the road. They'll mow down the incoming infantry from there.
Get your defenses going and your cash flowing in, and start training mammoth tanks. Amass an army of fifteen or more, along with an escort of ten APCs. Acquire the rail gun technology from the tech center for your mammoths while you wait on them to be constructed. While all this is happening, try to keep your base defended. The expansion to the east can be tricky to hold, as many NOD vehicles like to attack there. The largest problem is protecting the entire field from nasty stealth tank ambushes so that your harvesters can farm peacefully. A good method to try is to keep the battle base close to the field, along with the tanks.
When your army is ready, push them to the north, keeping the APCs behind the mammoths. Build reinforcements for later back at your base. Use the mammoths to clear the obelisks and head into the base. From this northwestern corner, NOD has many infantry defenses. Roll your army right over them, relying on the APCs to pick off any stragglers. Commence to destroying the base, peeling back the layers. When the ion cannon is ready, you can pause to build one. Use it at your leisure. It's not necessary, as the entire base doesn't need to be destroyed. You must only destroy the three shield generators. The most well-protected generator should be attacked from the side it is on. There is no sense even entering the core of the base. Attack from the west and smack down the generator quickly. When you need reinforcements, send them. Try to make sure they go in from the right angle though, there's no sense in them dying from obelisks on the way to play hero.
Once you've destroyed all three generators, central command will order you to use the Ion cannon against temple prime (via a cutscene). It is a simple objective, you only really must point and click. There is a beautiful full-motion video as the tiberium detonates, killing millions.
As far as the secondary objectives go, capturing the buildings is a cinch. The hard part is getting the avatar to be destroyed by the commando. There are a few in the NOD base. I suggest you try to focus your tanks on something else while you use jump jets to land next to an avatar and hope he gets it in time. Alternatively, if you've taken a long time before you've begun your assault, I noticed that avatars eventually start attacking your base - notably the one to the east. Use that to your advantage if you're having a hard time getting this tough objective. Good luck.