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The beasts were different from how the grimoire and summoners rank up. The latter two could only increase their rank or grade through battles, but beasts can also rely on consuming items or natural treasures found in the wild to increase their rank and grade. In return, this also meant that increasing their rank was not as easy and swift compared to the summoners.
Aside from very common beasts and beasts that have been studied already, most beasts' evolutionary path was actually unknown to everyone else. One would only be able to learn of it through trial and error, or by pure luck.
When it comes to evolution, it also doesn't always end in positive results. If a summoner made a mistake and let its contracted beast consume items randomly, there were chances that they would evolve backwards instead.