Guide: Fastest way to win
As soon as you gain control of the Hunter Killers, the Torrasque, and the Devouring Ones, clear up the left side of the map, but be sure to stay out of the Terran Base. Build two hatcheries (not at the same time though; once you control a drone, at least one drone must live or the game will fail you). When the hatcheries finish, start making an extractor, drones and overlords, as well as a spawning pool. When the pool finishes, upgrade both hatcheries to lairs. When they finish, evolve overlord transportation and speed. When you get 24 speed upgraded overlords, load up your hero zerg units, fly up the right side of the map, and charge right through the Terran Base, dropping your hero units on the Psi Disruptor. They are extremely hard to kill, and will make quick work of the Psi Disruptor.
Alternate strategy: Use the queens to win
The mission is a lesson in using the queens, as Guardians and other units are not available. Here's how to do it: Use the recommended strategy: (See above) Build four hatcheries, two on the west side of the map, and two on the south side. (starting location + two to the north + one to the east) There are more than enough resources to complete the mission. Alternate/divergent strategy: Build six queens. Place three groups of (12) zergling and hydralisk on the unguarded peninsula southwest of the enemy base. Place two groups of (12) mutalisk off the coast of that peninsula, along with the queens. Use the queens to 1. spawn broodlings the seige tanks and goliaths. 2. infest the two command centers. Infest the command center costs nothing, so the same queen can also be used to spawn broodling a tank/goliath. Invade with the three groups of zerglings and hydralisks, taking out the bunker and missile turrets, then attack the command center, using a queen to infest it. Then start building infested units. Be careful not to have any of your units close by when attacking with infested units, as they will cause unilateral damage. You can waste a whole group of friendlies if you're not careful. Bring in your two groups of mutalisks to defend your new base.