Outbreak

If you haven't already, visit your lab and purchase some upgrades. There are separate upgrades for both Zerg and Protoss research, and each has their uses. None are certainly better than another. Pick the ones that better fit your own play style, as buying one will block off the adjacent ability. In the mission itself you'll need to take out the buildings infested by the Zerg.

You're safe to explore the area and kill anything during the day. However at night, the Zerg will storm your base at night. You'll want to build up barracks and medics to help defend your base at night, while the speedy Hellions will be your main source of daybreak offense.

Successfully clearing an area of Zerg will help reduce their offense during the day, so be sure to clean up the whole enemy base before fleeing for the night. Likewise, a cleared out base can be reaped for its remaining resources. Even while trying to be offensive, be sure to not neglect your nightly defenses. While there is a wall to the south, the Zerg will eventually break through. Be prepared and make an additional bunker wall to protect your forces.

There are some bonus objectives that can only be completed at night. For these, make sure that you've first taken out a large amount of Zerg buildings and have a strong force ready to fight the nightly enemies head on. With an imposing enough army, the Zerg will be no match for your clean sweep of the planet.