Hello, Masters Protoss here with a brief tutorial and guide on how to defeat mutalisk play from zerg, something that gives a lot of players an incredible amount of trouble at all levels, and especially at the higher levels. This guide assumes you are using a forge fast expand. If you are not, you are going to be in a lot of trouble, you will not have the economy needed to defend without a special trick. Generally speaking, if you are not going to forge fast expand, you should do a 2 gate/stargate expand, as it allows for a void ray to hold off a bust on your expansion and to build phoenixes early enough to crush fast mutas. Do not go responsive phoenix however, unless you already have some out.
The first and most important tip I can provide is active scouting, and understanding of how zerg plays. Typically, mutalisks come into play off 2 bases with a spinecrawler wall in order to protect himself while he stockpiles minerals and gas to build the mutas. The spire build time takes a long time. In this play style, the zerg will usually pop 8-10 mutalisks and send them straight to your base.
Against this style of mutalisk play, you have pretty much two options, and one of them is scouting dependent. Unless you spot the spire building with an observer or hallucinated phoenix, this option is blind and risky, so I suggest avoiding it. If you do spot the spire building, the strategy is to do an all-in off of a fast expansion with pure gateway units, usually 6-8 gateways. Fast +2 weapons and blink is a very strong variant that will usually win the game in this case. Alternatively, zealot/archon off of 8 gateways is EXTREMELY potent against this. Either way, you must have a twilight council, it should generally be built rather quickly in this matchup. Regardless, for this strategy to work, you need to hit right before the mutas pop, to do sufficient damage before they are out. Usually this involves killing all the spinecrawlers and the zerglings. By themselves, the mutas when they first pop will not be sufficient to defend, and you win right then. However, this variant is dependant on a couple of factors. Some zergs have started throwing down a roach warren just in case, and deciding not to build the mutas if they detect an all-in. If you start seeing roaches, you should back off and expand with your army, you should be able to defend, and you've got the tech to deal with mutas.
The second variant of muta play is when the zerg responds to your fast expansion with a fast third of his own, then opens roaches to defend, while building the spire. He doesn't stockpile money, so fewer mutas pop out, but with the income of that third base they very quickly get to the same muta count as they'd have off two bases. This variant is extremely hard to kill with an all-in, but if you can snipe one of the bases you'll be in great position.
The second and safer way of battling mutas requires a lot of careful maneuvering. Essentially, you are going to turtle in your own base. If you wish to use this option and you scouted the spire building, you should immediately take a third base if the mutas aren't out yet, and throw down a couple of cannons at each base. Get blink ASAP if you don't have it, and defend with stalkers. As soon as you can afford it, put down a second forge. If you couldn't get the third base, you'll have a harder time of it, but your strategy is the same, cannons at each base, blink stalkers ASAP, get second forge, and turtle until you can take your third. 2 forges is very potent against ling/muta, but not good against other zerg strats, that's why it's reactive.
All while doing this, you should be building probes, leaving stalkers in a good position to defend the mineral lines (generally in a middle position or split up with another group able to reinforce quickly), and attack mutas when they show up. Try to blink as they run away if you can, although if you're out of position you can blink in to attack to prevent damage. Your goal at this point is to get to high templar and research storm as fast as possible. Once you get high templar with storm, you are able to finally leave your base, although you should still aim for around max supply. You want to leave 1-2 templar in each base and storm mutas when they show up. 1-2 storms will usually chase the mutas out of your base for a long time, since they'll be so low on hit points your stalkers will annihilate them. If they take 3-4 storms, you'll likely wipe them all out entirely, which puts you way ahead.
The entire time you are doing this, you should be scouting, particularly for a greater spire. You must know brood lord timings, if he hits you with brood lords when you don't have a mothership, you're in a lot of trouble. If you detect a greater spire, get a mothership ASAP.
Be aware that zerg will likely take the entire map during this time. Your goal should be to warp in zealots in various locations and snipe bases if possible. You can use DT's, but their cost makes it very hard, and if you lose them without killing bases, you're in a lot of trouble. If you do not think you can manage it (don't want to risk a warp prism with mutas out and no pylons on the map), you'll have to let zerg have the bases, if you go after them with your army you're dead by counter attack, and if you go after them with just zealots walking from your base you'll lose them. At this point, your goal should be to go straight for the zerg main and kill off the tech structures, while bringing some high templar with your army. Kill the tech, and it doesn't matter how many bases he has, he can't make fighting units.
Here's a replay from today, I'll post more when I play some more out.