From Halopedia, the Halo wiki
Quickly rush down to the south and start up your base. As you're moving down south, be sure to check out the first stairs on your right and check out that area to find the 5th Black Box. Use the Scorpion Tank to hold up the enemies while your other units fall back.
Head for the base area and quickly garrison any Marines at the Crashed Pelican Garrisonable Center (which gives them better protection). Quickly set up 2 reactors, a Barracks, 2 Supply Pads, UNSC airpad, Vehicle Depot and four turrets.
Upgrade your Supply Pads to Heavy to fasten your resource replenishment and work your way up from there by creating a bunch of units. You'll be under constant attack by the Covenant, so you'll want to garrison more Marines at the Pelicans to the north. Set up a few Scorpions and you should be able to hold out for quite some time.
When Omega Team arrives, have them - and some Scorpions and other units you can spare - set foot for the 2nd base terrain on the west, and take out the Covenant mega turret here. When you've done so, start building your 2nd Base and secure the area. you need to build a Field Armory to upgrade your turrets as this base is more vulnerable to enemy attack. Just south of the 2nd Base is an abandoned Reactor in which you can garrison a Marine Unit to increase your tech level.
To collect the Skull in this level, send a unit over the road located on the west of the 2nd Base and find it in a desolate area.
Build up a small army of Scorpions and maybe some Wolverines (if you want it to be easier) then send them - together with several aerial units, Marines and Omega Team - over to the Covenant Base. Target the troops and turrets first, then focus your attention on the base and it'll fall soon enough. Kill the Factory first as it can constantly produce Wraiths. If you use the barrage ability of the Wolverines it should work better.