I have Guepard, my galactic tigrean. He was adopted from the pound. But I noticed that there wasn't a galactic potion. How do you get a galactic pet?

On the 6th and 7th of each month you can dig for gems in Coda Caves, you can also visit Itallo and do one of his quests, he'll ask for up to 5 random gems which you have to bring him to make your pet galactic.