Give the monster things he can do to the environment that impede the hunters or empower himself.
For example, a monster that likes light will want to break open the shuttered windows. A monster that doesn't need to breathe will want to flood the area with poison gas. A monster that can see players on its minimap as long as they're touching a plant, will want to place down moss and ferns and stuff.
So if the players start seeing this behavior, these traps, these ways the monster has modified his environment, they will get hints as to what kind of monster it is. Of course, the monster might be able to trick them by doing things some other monster type would do ...
Monsters should leave behind traps and stuff too. And I like how the Hidden can staple slain hunters to the walls and ceiling to unnerve the survivors.
I suggest that slain hunters get to view the action from a survivor cam, so they're not just kicked to a lobby. But one survivor ability - or use of an altar ritual or something - should bring a slain hunter back as a ghost that must stay near (the altar / its slain body / its raiser) rather than being a respawn or free-roaming cam.
Generally, make special abilities things that any hunter can do with the things in the environment - but he needs it just the right way. He needs ingredients, he needs the clouds to part so he gets good moonlight on the altar, he needs silence or music, etc. And the monster can deprive them of those things if it knows where to go and wants to risk being caught.
Monsters should rely on ambush. If the hunters find the monster out in the open in a room or hallway, they should have a good advantage. I guess that means I'd like to see the monster be fairly weak but fast, or invulnerable except for a limited resource that the hunters have, or it has a limited strong attack that it needs to regenerate.
For example, a werewolf may have a special attack but otherwise just mauls for little damage. The normal mauling mainly shoves the guy away. The power maul does real damage. But to recover his power maul he needs to bathe in direct moonlight (so if the clouds are over the moon he's screwed). Fighting a werewolf in moonlight is the bad idea. The players need silver arrows and silver swords to hurt him. But silver arrows can break (50% per attack), and silver swords can bend (10% per attack). Arrows are non-fixable but you can straighten a sword in the smithy - which is outdoors in the courtyard, a prime werewolf-ambush site. Arrows and swords are hidden around the map in various places, some of which the more-agile werewolf has better access to than the hunters. Do they split up and gather as much as they can, or stay together in case the werewolf attacks?
The Hidden is invisible and can leap and sprint. But he can be seen by hunters as a shimmer, which lets them hit him if he's too slow. The Hidden has low health and only a melee attack, except for a very limited supply of grenades (I think 1?). He can regain health by chewing a corpse, but he can't get more than like 30% health from one corpse. The hunters have strong weapons but just getting hits is the problem.