Mica Magicog is one of the resources you can find while exploring Final Fantasy XIV's Dawntrail expansion. The way you unlock it comes down to tracking a specific creature and defeating it with a strong group of allies, and you only have a short time to do so.
Mica the Magic Mu | Mascot Murder FATE Boss Guide – FFXIV
Not every monster you can find in the world will appear regularly. There are specific steps you need to take before they spawn, and even then it can take a few hours for them to appear in your Final Fantasy XIV world. The creature that drops the Mica Magicog is a powerful foe, and knowing where to find it is important. Just make sure you bring enough friends with you to take it down.
Mica Magicog is earned by defeating Mica the Magical Mu, an enemy encountered during the Mascot Murder FATE in Final Fantasy XIV Dawntrail. You can find this enemy while exploring the Living Memory area, the final region you unlock in the expansion. After unlocking all of the sections in this region, you'll need to track down the Aether Currents in Living Memory, as they prove vital to taking on Mica the Magical Mu, allowing your mount to fly, making travel much easier.
After you've collected these, the next step is to find the specific FATE activities that deal with Mica. There are two that you need to do, and they appear one after the other. You need to do these two FATE activities to summon Mica the Magical Mu in Final Fantasy XIV.