StarCraft/Terran mission 3: Desperate Alliance

You don't have to attack anything in this mission: you simply have to survive. This isn't as easy as it sounds. You'll be facing air units for the first time, but really they're not very hard to kill. After you have a strong resource chain, fill up your existing bunkers with three Marines and one Firebat each. Then build two more on each base entrance as the mission progresses. As for unit production, you shouldn't really build Factories; all you can do with them in this mission is build Vultures, and they're not particularly useful. Instead, have two or three Barracks going, all producing Marines and Firebats.

Also, build two Missile Turrets in each base entrance. These and the bunkers' Marines will pretty much shred all Mutalisk attacks, but just in case they decide to go over the roof of the building protecting you, you should put at least 12 Marines on the roof (you can't build anything up there). Even if you think you've got enough defenses, keep building units. You might have 100+ supply worth of infantry in this mission: all the better for you!

For most of the 30 minutes, Zerg attacks are light. This is because they're saving up their forces for a final assault. With 2 minutes remaining on the counter, the Zerg will launch a massive attack. Expect a horde of more than 50 Zerglings and loads of Hydralisks and Mutalisks. This is exactly why you created as many units as you did. You should be fine, but if the defensive line is broken in a base entrance, lift off all buildings and move them in different directions on the map. This makes it impossible for Zerglings to do anything to them, and will buy you time. When the camera shifts to an edge on the map, your rescue has come.

Aggressive Method
There's a way to see some more action if you don't want to sit tight in your base. Although it's not necessary, you can actually attack the Zerg and prevent them from creating that huge army. This is not recommended for new players, simply because it can be very difficult to pull off. What you do is after filling up two bunkers at each base entrance, have three Barracks produce two to four full groups of Marines and one full group of Firebats. Also, upgrade Marine range and Infantry Armor and Weapons. Send this force north from the right entrance to take out the small outpost there, and basically mop up the Zerg bases. You might run into Sunken Colonies, which will kill Marines in only a couple shots, and you must focus all fire on these structures if you do. Keep producing units at your base in case this attack fails. Finally, if the attack force is not ready by minute 20 at the very latest, scrap the attack. The massive horde will pretty much be done, and all you do will be to enrage them.

If you can manage to wipe out the Hydralisk Den in the upper left hand corner, it should be easier to take out the base as they will no longer have Hydralisk reinforcements.