After you scout it, even if you didn’t plan on going that, start a Twilight and start+ chrono boost Blink immediately, turtle on batteries if you need to. When engaging, pull the unit that is locked out AWAY from the Cyclone and not towards. You want to break Lockon as much as you can, and none of your units can catch his cyclone anyway even if you walk towards them.
After Blink finishes, you blink on top of the cyclone and focus fire them down. They are very expensive units. You can also wait until Lock-on happen before you blink forward since that will also break the Lockon. After that go mass Chargelot Archon. As long as you didn’t take too much loss he shouldn’t really have anything that can engage Chargelot Archon that effectively.
Also, never forget making workers and macro even when under pressure, because a lot of the time that’s actually how you lose the game.