This isn't nearly
as bad as what you may be expecting.
At the end of Chapter 2
you will gain a pet summon ability on one of your characters. You unlock new summon transformations for this pet by returning to previous locations and fighting a battle.
Every time you finish a story fight, scroll around the world map and look for any location which has a large silver side quest
icon to the left of it. This means there's a new pet transformation available at that location!
You don't have to do anything special at all. Simply return to the location which will autostart a battle; win the battle and you get the new transformation. If the side quest icon stays on the world map, it means there's another pet to collect there. Go straight back in to fight for the next one!
You can check how close you are to collecting them all by pressing
from the world map screen, and scrolling down to pet