evolution

It depends where exactly you are in the game: if you've at least gotten to Asgard, then you could find out the basics about monster evolution. The key to evolutions are the food, level, and (possibly) statues. In practically every area after Asgard, you would see a person(?) dressed up as a cat, calling themselves a Katz. Then, when you talk to them, a menu would open up, and there would be three options: Party, Cooking, and Quests. As you go around to more places, you might be able to find someone called a Wonder Chef in multiple areas, who gives you a new recipe each time you find him. The recipe and person cooking will change the stats accordingly. But the main point is that when your monsters are at a high enough level, then a symbol will appear near their avatar when you open up the main menu screen, indicating that they can change class, or 'evolve'. All you need to do is feed them while they are like that (in other words, go to a Katz and cook something for them) , and you get the option to change their class. I hope this helped.
P.S. evolved monsters will regain all skills learned previously and 20% of their stats. Some will even regain their artes. However, they will regress back to level 1.

To evolve your monsters, you have to look in the game menu and see if there is a yellow monster-face like sympbol beside the picture of you monster in your party. When your monster has that symbol, that means you can evolve your monster. Although you need to go to where you can find any Katz people roaming around the place where you go. By then, choose COOK and you will need to cook dishes. Although to cook, you need to find chefs roaming around random places to equip recipes, and you need the needed ingredients to cook. I hope I helped.)