StarCraft: Brood War/Terran Mission 6: Emperor's Flight

Getting Started
The introduction to this map is a war scene where Valkyries are taking out a huge group of Mutalisks. While they are fighting, two dropships will drop two siege tanks each in siege mode, on the opposite cliffs. When the Mutalisks are taken out, all the units will be given to you. You will notice that you have many units, but no supply depots. The first step would be to have at least two of your SCVs building supply depots in your base, while the others can gather minerals or repair your vehicles.

Once you have enough supplies, start building siege tanks. Once you have enough siege tanks, feel free to take out the small area occupied by the Protoss in the northwest cliff from your base. Take your Valkyries with you, since they have a few Scouts begging to be destroyed. Once that is done, you are entitled to a rich 13-mineral field patch with a bountiful vespene geyser. Expanding here will get you far, as long as you remember to set up defenses to the north, where you will find Brown Zerg.

With your two bases, you should have at least four factories pumping out siege tanks and goliaths, which you will find very useful for both attack and defense. Have your SCVs build many missile turrets all around, as the Zerg will harass you with Mutalisks.

Thanks to the Warp Gate, you will find the Zerg and the Protoss fighting each other, and you will have constant vision in the Warp Gate area.

The Attack
An ideal attack involves one group of Goliaths and one group of Siege Tanks. There are many paths you can take; the main entrance to your homebase will take you to many cliffs, all leading to the Warp Gate. You can also head north to where the Brown Zerg is; there is a path that will also take you to the Warp Gate. Once you are there, conduct a massive all-out attack against the Protoss until you reach the command center. Don't hesitate to use your Valkyries against the few Carriers they have.

Thanks to your simple objective of destroying one Command Center, you can also choose to just stay in the defensive and train battlecruisers instead. If you have one group of battlecruisers with Yamato Gun (and enough energy to fire it), you can just head to the command center via the water (the lake that separates the brown Zerg base from the Protoss) and just shoot the Yamato Gun at it. Even if you lost a battlecruiser or two along the way, you can still win with this strategy. If the command center is still alive, have your battlecruisers just madly attack it until you kill it or until all your battlecruisers are lost. If you are losing all your battlecruisers, click on the command center to check its HP. If the numbers are in red, the command center will burn itself down slowly, and you will eventually win.

Alternative Strategy
Actually you can win this mission without even landing your buildings.

After the cinematic take up a SCV to the cliffs to repair the siege tanks (in my case, only the right tanks were damaged), unsiege them and load them up into the Dropships. Take your Dropships and your Valkyries (actually you can do without the Valks since you won't encounter any enemy resistance apart from one Photon Cannon). Well, and that's it - take your Aircraft to the northeast and follow the grassy valley until your reach the right edge of the map. If you are unsure, you can scout ahead with your Valkyries, but really - you won't (or at least you shouldn't) meet enemy units.

After you grouped your aircraft on the very edge, fly up along the right side of the map to the very top - along the way you'll fly past the Photon Cannon mentioned before. I took the Dropships past it separately, so each one was damaged to 93/150 HP (it got hit by three shots), but if you group them up with the Valkyries, you could get through with even no damage to the Dropships. However, after you've reached the upper right corner of the map, unload your four Siege Tanks between the Probes, deploy them into Siege mode and, well, win the mission and enjoy the cutscene!