I'd have to go with a public land P&Y animal of just about any species. Killing a mature animal that has horns/antlers of XXX inches taken with a bow on public grouns .... mighty hard to do in many areas.

Toughest animal I've hunted ? P&Y / mature whitetails on Arkansas public ground. I've antelope hunted, mule deer and elk hunted and have had success with rifle/muzzleloader and bow - but taking mature whitetails with archery is the toughest so far.