Halo Wars

As simple as it sounds. Complete the mission only using your original base. Do not start up any new bases.

You will probably need to build supply pads to up your resources, and then recycle them to build the other things that you may need. Still not too bad as the achievement can be done on easy.

Here are a couple quick tips for when attempting this achievement.

First, play on easy.

Second, give yourself a strong initial force when going up the hill i.e. about 4-5 scorpions and make sure you move quickly before the Covenant reinforce the first base.

Third, once the tanks leave, recycle the vehicle depot and replace it with an airfield. From here on out, just keep building vultures and hornets, as they can bypass the hills and just catch up quickly to the elephant.

OK so just to let you know, I take nothing away form the other solutions here, but I'm the kinda guy who likes direction and details, so heres\'s my take on this or it's what I did.
Strategy games are all about multi tasking and this guide is for those not so great at this type of game, people like me.

During this mission you will only need to build: 2 Reactors, a Field Armory and an Air Pad (*Field Armory is optional)

You have to remember, non upgraded supply pads are very cheap so that by the time you recycle it it will have doubled or more the money it cost to build. I'm telling you this because you will not be upgrading just one of your supply pads.

So let's get to this. Put your self on easy and when the mission starts move all your initial force up to the fallen core, otherwise it will start to get attacked and it does have a health bar and will (eventually) blow up thus making you fail the mission.

Even though you can DO NOT make your elephant yet.

Put your rocket Spartan on the left of the core along side the mountains cliff (he's very effective at taking out the Vampires which will start attacking. Along with one of the mobile units. Then put your machine gun Spartan in front of the core along with Forge (they will take out anything coming down the hill) The sniper Spartan should go just to the left of Forge and then the last mobile unit (both these units will also serve as back up making your Core very safe.) Now DON'T move these units until I say..Even if you here the lady tell you the Core is taking damage.. just let them take care of it..trust me just leave them be the Core will be fine.

The only person you can/should move is Forge since he's fast, you can circle the base and pick up the supply crate around your bases area, but DO NOT go up that hill! After the supply crates are picked up put Forge back where he belongs.

Again, DO NOT make your elephant yet!

Now on to the base. Start by upgrading to a Fortress which will give you 7 open pads to build with, now make 5 supply pads and 2 Reactors. Don't worry about turrets the enemy will never get that close.

You can and probably should check on your Core and the units surrounding it and heal them if they need it, all the time I did this they never really needed it though.

Once the reactors are up go ahead and recycle one of the supply pads, (remember that supply pad I told you not to upgrade) and create a Field Armory. After the Field Armory had been built recycle another supply pad and build an Air Pad.

Once you have enough money start upgrading in this order:
Reactors
Air Pads: Everything for your Hornets and Mega Barrage for your Vultures.
Field Armory: Reserves, Reinforcements and Twin Engine.
You can also upgrade your MAC rounds but you shouldn't need more than 2, they will reload as you move up the hill.

Now back to the Air Pad and make 7 hornets and 3 Vultures.

Still don't make the elephant.

*(Optional Field Armory) If you feel comfortable with the money you can recycle another supply pad and build a Field Armory and make a scorpion, but they are slow and you probably won't need them.

Once everything is upgraded take JUST the 7 Hornets and the 3 vultures and fly them up the hill slowly directly in front of the core, leave all ground units where they are at!!! You will encounter a few units along the way so go ahead and slow down long enough to take them out and then keep moving up.. and take out the first Covenant base. Target the turrets first, with as much combined fire power as you have they will go down fast and don't be afraid to use your mega barrage. Throw a regeneration/repair on them if they need it and you can further support them by sending down a MAC round. I took out the first base with no casualties but one Hornet was pretty messed up.

Now send Forge up the hill and park him right behind where that base was BUT DO NOT BUILD ANOTHER BASE!!! The enemy will begin to rebuild the base and they will send a unit or two to try and kill Forge but he's tuff and will survive, he will also ensure the base is not rebuilt by constantly destroying it as it regenerates. This is also where the optional Scorpions come in. You can back up Forge with 1 Scorpion.

When your ready move your flying units following the path, again they will encounter a few units and again stop to destroy them...now move on and the next battle will be with a small contingent of Flood. Take these out and continue up following the path. At the top of the next hill you will encounter a 2nd Covenant base, same drill target the turrets and take it out. Don't forget you have regeneration and MAC rounds at your disposal. Once gone DO NOT BUILD ANOTHER BASE and you need to leave 1 of your Vultures at this base to ensure it does not come back.

Ready for the final big push? Check your flying units if you have lost anything now is the time to replace it. You can now also go ahead and make your elephant you can even hook hook it up , but DO NOT BEGIN TO MOVE THE CORE YET!

Once you have 7 Hornets and 2 Vultures keep following the path and up at the top to the left will be the final Covenant base. Take it out as you have done the other two, you may suffer a little more on this one without the extra Vulture but that extra MAC round will sure help a lot now too.

Again DO NOT MAKE A BASE!!!... Leave another Vulture there and move 7 Hornets and 1 vulture back down to where you fought the Flood, as they will have respawned by now.

Meanwhile back at your base (hook up the core to the elephant if you have not already.)
Now select all the local units down there and then select the top of hill at the platform and sit back and watch as they move unhindered by ANY enemy to finish the mission and wait for your achievement.

Here is my thoughts on a run thru on Heroic in Par time. I have not yet done this so take it for what it's worth. If I can get this done I will re edit this solution to say what I did.

Go ahead and make the Turrets on your first base and even upgrade them to.
Upgrade to 3 or 4 MAC rounds as well.
When you defeat the first base MAKE A SECOND BASE and start with supply pads and turrets upgrading them.
Then just fly directly to the second base.
Don't worry about the Flood until after you have defeated the third base, MAKE A THIRD BASE and more supply pads turrets upgrading them.
Go up the hill and take out the third base and again MAKE A FOURTH BASE with and Air Pad, probably won't need turrets but if you want and think you have time go for it.
Then move to take out the Flood AS you move your elephant up the hill.
You may also want to reinforce any vehicle units by placing the Spartans inside them as they (Spartans) move slower than vehicles and if you have them grouped together with your vehicle on foot they may slow you down costing you extra time.