Main Objective: Destroy All Protoss Shuttles [8 waves remaining], No Shuttles Can Escape
Bonus Objective: Destroy the Stasis Chambers [0/3]
Shoot the Messenger: Complete the "Shoot the Messenger" mission in the Heart of the Swarm campaign.
Warp in Peace: Don't let a Protoss Shuttle being Warping Out in the "Shoot the Messenger" mission.
Extreme Nexism: Destroy 2 Protoss Nexuses in the "Shoot the Messenger" mission on Normal difficulty.
Work on your economy and start harvesting gas. There's not much you have to worry about until the first shuttle arrives. Hydralisks will be your main means of dealing with the Protoss air units in this mission.
Even though the next shuttle has a fighter escort, it is quickly dispatched with a few hydralisks. You should have a macro hatchery by now and started working on ranged upgrades. Adding a few spore crawlers by the warp gates will also be helpful later on. Start making your way to the closest Stasis Chamber.
The closest Stasis Chamber isn't very well guarded and is easily destroyed with what units you should have by now.
With the next shuttles incoming, head towards the warp gate east of your base. It will reveal a frozen protoss nexus which transforms into a free expansion once you clear the zealots.
After you destroy the shuttle, it will give you time to clear a path to the eastern warp gate and stasis chamber. This chamber is guarded by a high templar, so watch out for psionic storms. This is also a good time to build drones and saturate your new expansion.
The shuttle escorts start to increase in strength from here forward with Carriers joining the fray. Don't forget to replenish your army and continually add to it when the income is available. If you find that you're sitting on an excess of minerals, start building spore crawlers by the two eastern warp gates, as those are the final destination of the last wave of shuttles.
Spreading creep by the two warp gates to the east will help increase your mobility and deal with incoming shuttles. The remaining waves consist of multiple shuttles and fighter escorts trying to warp simultaneously, so mobility is key. Start connecting the two warp gates now. The next shuttles will be towards the two warp gates surrounding your base, so if you've been spreading creep from the start, there should be enough covering those areas already.
Now is a good time to start clearing the area towards the final Stasis Chamber as it's very close to the path of one of the incoming shuttles. You should also have enough time to make your way back and deal with the other shuttle
After clearing the shuttles, head towards the final stasis chamber. Clearing out the protoss structures directly southwest of the stasis chamber, will open up another potential expansion. By the time you're finished clearing this area, two more shuttles will launch.
The next wave intersects in the center of the map. This is an easy location to intercept both shuttles without much extra movement. Rally additional hydralisks there from your hatcheries. Also, you will most likely have a bank of excess minerals by this point. Use it to build spore crawlers to help you defend the warp gates. Two more waves remain.
This wave intersects at a much higher point than the last. It will be easier to intercept the shuttle heading towards the southwestern warp gate first, and then head to the one heading towards the southeastern warp gate afterwards.
The final wave will consist of 3 shuttles all heading towards the same gate. There will also be a mothership escorting the shuttles. With a forest of spore crawlers and an army of hydralisks, this wave shouldn't pose too much of a problem.
Once you deal with the first shuttle escort which consists of colossus, the remaining shuttles and air escorts fall easily to your hydralisks and spore crawler forest.