As others have said there are different monsters to kill, you get a random one. The easiest one is the mammoth, but there is also a snake in the water, 2 different kinds of trolls on the hill behind the mammoth area and a wamasu somewhere else.
You need to look for which one you got. On the other hand, you can always leave the hunting grounds without finishing the quest, wait some minutes (I think it's 5, but to be sure, better wait 15) and go back it. It will be reset by then and you might get another of the monsters.