Domesticated Hydra

“Monstrosity N” means “If this permanent isn’t monstrous, put N +1/+1 counters on it and it becomes monstrous.”

Monstrous is a designation that has no rules meaning other than to act as a marker that the monstrosity action and other spells and abilities can identify. Only permanents can be or become monstrous. Once a permanent becomes monstrous, it stays monstrous until it leaves the battlefield. Monstrous is neither an ability nor part of the permanent’s copiable values.

If a permanent’s ability instructs a player to “monstrosity X,” other abilities of that permanent may also refer to X. The value of X in those abilities is equal to the value of X as that permanent became monstrous.