You start with two hatcheries, so this mission can go pretty quickly. Another thing of note is the protoss photon cannon just southeast of your base. Avoid it early on, for it might cause you some needless losses. Now, set both hatcheries' rally points to the same location so you'll be able to more quickly mass produce units without them getting in the way. Have a total of ten (or more, if you like) drones to harvest minerals and get six on extracting vespene gas (the geyser's farther away). You have some new units you can make now and gas will be more important in this mission. Also, as you have two hatcheries you can produce units much faster, and your minerals will go down rapidly as you make them - thus the extra drones. Lastly, group your starting military forces into a group to help defend your base. The protoss will attack, but not in great force. For that reason you might want to build a sunken colony or two spread out to help hold them off while your forces respond.

Build up your base, taking mind to upgrade one of your hatcheries to a lair. You can build spires that way, which enable you to make the mutalisk zerg standard flying unit. You'll want some of them, as they're quite fast and the damned protoss zealots can't touch them! Get the carapace upgrade at your evolution chamber and start pumping out military forces. Get about 12 zerglings, eight hydralisks and eight mutalisks to start your attack. Send the zerglings southeast with the mutalisks and hydralisks just behind. Have the zerglings focus their attacks on the dragoons, then the photon cannon. Your mutalisks can avoid damage as the protoss will probably be distracted. Have them help. The zerglings will likely be destroyed, but you should be able to finish off the protoss here. When you've finished off their buildings, push further southeast.

You'll see another minor protoss base, which when destroyed will allow you to rest for a moment and replenish your forces. Make sure you have a mirror of the force you started with and you'll be just fine for the next battle. The important thing is that you start the attack with these forces but continue to pump out hydralisks (if the hunter killers back at your base come under your control don't hesitate to use them!). Move the rally points of your hatcheries around with your forces to keep a steady flow of these coming to assist you. If you've hotkeyed your hatcheries as I recommend in the general tips section you won't have any problem switching to them without moving your attention from the battle.

Destroy the protoss base west of the resting spot and you'll basically be home free. Rest your forces for a moment while you get a drone to pick up the chrysalis. Bring the drone south (have some of your hydralisks or the hunter killers escort it) to the ramp southeast of the protoss base you destroyed. Lead with your forces and follow the path, where you'll eventually come to the beacon. Just remember to keep the drone with the chrysalis safe and you should be fine.