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Hmm... I have another idea. Instead of a hydra, let's use an underground drake. Its shape would be like a worm, long and elongated without limbs, with a dragon's head and similar body covering. As for how it moves, it would be underground.
That is, when it needs to attack someone or move to another location, the creature burrows into the ground and emerges in the cell where it needs to be.
Its special ability would be tunneling, analogous to a griffin's jump, but underground, and the time spent out of combat would be one turn longer than the griffin's ability.
As for hippogriffs, IMHO, having two riders in the army would look organized and formidable. In the human army