One guy's opinion: most of what is missing from hunting missions in video games is "the thrill of the hunt." Learning about the target, following it, catching your first glimpse. Something in there that appreciates the majesty of the thing you're about to kill. I'm not a hunter IRL, but I live in the southern US and there's a paradoxical "love" of the target that is missing from most hunts in games, though it was definitely there in Shadow of the Colossus, and there are glimpses of it in Monster Hunter. I guess the key is - give reasons for players to learn about what they are going to kill, and in doing so create empathy for the thing they are killing.
That's good thinkin'.
It'd be pretty cool if you were just given clues about it: its footprint shape, what it eats, things like that. Maybe not even a picture, just a silhouette or a description. Or a drawing. And not like an accurate one: one from a confused or scared person, or one working from hearsay, or a child's drawing.
(I've never been interested in playing hunting games, but if one came along where you have to hunt down monsters based solely on children's renderings of them, then absolutely.)