This and the next two Zerg missions are going to be pretty straightforward.

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Here's the sixth mission in the Zerg Campaign in StarCraft.

[MISSION VI: THE DARK TEMPLAR]
- Exterminate the Protoss intruders
- Kerrigan must survive

After the main Protoss base is destroyed
- Bring Kerrigan to Tassadar's challenge alone

Very straightforward mission - you start with a decent defense force of Kerrigan, four Hydralisks, two Mutalisks and two Guardians. Have your Drones start gathering resources and build up your economy by adding more drones and adding more supply with overlords. Station Kerrigan and the Hydralisks near the right entrance of your base since most attacks will take place there.

You can also send your fliers down south of your base to remove some Protoss units stationed in a potential resource expansion. Upgrade to a Lair and upgrade Ventral Sacs to access this expansion. Make sure that you have your base and your soon-to-be expansion well-defended with Spore and Sunken colonies by the way.

My main method of attacking the Protoss base in the southeast is by air. I decided to build up my economy until I can get a Hive and have double Spires (once becoming a Greater Spire) and get Flier upgrades completed. My attacking force towards the Protoss is mainly a mix of Mutalisks and Guardians. Guardians can just hit stuff from a long distance while Mutalisks deal with the aerial threats or can lure out enemies.

A new mission objective pops up once you destroy the Protoss base. Bring Kerrigan to the center of the map via Overlord and have her attack Tassadar. At this point, just sit back, relax and watch the show. The mission ends in a victory afterwards.