Hotkey your starting units to defend your base, for some zerglings will attack soon. Warp in 10 probes for minerals and three for vespene then get your basic needs: a gateway (make it two for faster unit production), forge and cybernetics core. Start warping in some dragoons as soon as you can (you will need pylons but those should be done for powering your previous buildings). While all that's building, send your defenders to the north and take out the zerglings that have burrowed there. You'll see a ramp, which is a good place for a photon cannon/pylon combo. Place it on the cliffside so the zerg have to go further to attack it. Another good spot is to the east of your base where there is yet another ramp. These are the only land entrances. Some dragoons can be used to defend against any possible air attacks.

Upgrading your plasma shields (pick attacks as the second upgrade) would be a big help to you, and getting the singularity charge upgrade for your dragoons is a must. Build up about twelve zealots and six dragoons to help you attack the zerg. But they should wait for the prime time, which is after Fenix arrives. Just hold off the zerg with your units until that time. If the units I recommended get done before you're out of time and you have the resources, keep building more! There's no reason to finish the mission and have resources left over. More zealots will really help as they can run about into the Zerg base and distract them.

When the countdown reaches zero, Fenix arrives with a small army, including three reavers! Oh yeah! Build scarabs for your reavers and, keeping them in the rear, move down the ramp with all those units. Just keep in mind that you'll have to replenish the scarabs of the reavers. Have them all in one group and press r and they'll all build one more. On this mission, they can hold a maximum of five. Kill off the zerglings then pause to consider your attack.

You can send in your forces at your base to attack from the west, while the forces of Fenix attack from the east. Use the western group to attack first as they might distract some of the zerg. Move fenix's group south, but try to keep the reavers doing all the work in destroying buildings while Fenix and the others protect them. Concentrate the reavers on sunken colonies and masses of units. You'll need to keep your dragoons hotkeyed to take down mutalisks! Just be sure not to let your zealots wander into the base (Fenix's group, the others should run amok) as Fenix could be killed. Let the reavers do their jobs, and push to the south. The location of the cerebrate is south of where Fenix's group started their attack, at the bottom of the map. It's protected by many sunken colonies, but you know those won't stand up to your reavers.