Final Fantasy XV Sky GemstoneWhen you first get to Galdin Quay, you’ll see a cat on the boardwalk leading to the restaurant. Interacting with her will start the Kitty Catering quest. You’ll need to catch a certain fish at the nearby fishing spot (which appears only during the day). Offer it to her, then bring it to Coctura so she can prepare a dish. After you feed the cat, she’ll disappear.
The next time you meet her will be at the Cape Caem lighthouse, during the Brave New World part of the main story. This will start the Feline Feast quest, which will require you to find food for the cat, while keeping in mind how picky of an eater she is.
There’s a vendor at Cape Caem outpost that sells insanely expensive luxury cat food. You’ll need to shell out 20,000 gil, but the cat will be grateful. When you give her the food, she’ll reward you with a sky gemstone.
Important Note: You don’t need to spend 20K gil. Once you increase Fishing level, you can catch a fish and give it to Monica to fry it up for you. (thanks Ryan)
If you bring the stone to Cid, he’ll start working on the upgrade. You’ll need to wait a couple of days for him to finish, so you don’t have to stick around – go away and do something else until you get the call. If you know of another way to get this elusive stone, feel free to share it in the comments.