In mighty monsters , there are 5 types of rarity.
Rarer monsters have more base hit points and are more diffucult to capture.
Rarities, in increasing difficulty to obtain, are:
In the wild , you can't tame Ultra or Legendary monsters without a Master Gem of the corresponding rarity
Most monsters progress one step at a time during their evolution, although there are exceptions (like Ekko)
Catch rates with Taming Gems-
Common-MAX 75% Rare-MAX 40% Epic-MAX 15%
Keep in mind, only Stage 1 Monsters can ever be tamed