One last thing remains before the attack on Korhal's capital itself, the destruction of the Psi-Destroyer. This arcane structure is built to emit a field that destroys all Zerg within it, via their own psionic link. Fortunately, you have access to some troops that are not bound by that link. For this mission, you are given control of both Sarah Kerrigan and Dehaka. The primal Zerg has the important trait of being immune to the Psi-Destroyer and Psi-Disruptors that Mengsk is using to protect his forces against the Zerg Swarm.
You open with just Dehaka under your command. He is a large assault unit with an advantage against structures, the ability to leap cliffs like a raptor, and the Mend ability that Kerrigan can also field. Climbing through a ventilation shaft onto one of the Terran aerial platforms, he emerges near a small trio of marines. Slay them and move on to the Northeast, leaping up onto the platform above to destroy the siege tank. The first power link waits further in that direction- send Dehaka to destroy the thing.
The destruction of the power link temporarily disables the Psi-Destroyer, which allows Kerrigan to land a pair of hatcheries. You are then transferred to her and the base, where you need to gather up minerals, protect the outpost, and begin the assault against Augustgrad. Make sure to advance the Lairs to Hives quickly, so that you can generate more larvae at a good clip.
A small squad of marines will soon attack your first outpost from the Northeast. Rebuff them, and then take out and replace the Terran mining base to the Southeast with your own hatchery. Now is the time to invest in improving your unit basis- use Evolution Chambers to advance your armor and attack power while you entrench with queen-spawned creep tumors and various forms of crawler. Make certain that you guard your flanks and rear with spore crawlers as, while the Terran structures may not be present in those directions, it's a pretty sure thing that an end-run of air units will happen at some point during the mission.
As the reactivation of the Psi-Destroyer nears, Arcturus will send a second attack force at your main base- a pair of goliaths and some marines and marauders. These should be destroyed fairly easily, but form a large enough group to do a bit of damage to your defenses if you're not adequately prepared yet.
