Magua is a fierce and fearsome (and wily) warrior chief of the Hurons, but that is not why he is not afraid of the bear. Chapter twenty-five of The Last of the Mohicans by James Fenimore Cooper is set in a cave, and there are human characters as well as a strangely human-acting bear.
Heyward has been brought there to heal a dying woman, and he begins to make up some strange healing rituals. Each time he begins, the bear begins to growl disruptively. The Hurons in the cave assume the conjuror (who is visiting the village and is kind of like a witch doctor) is here in the guise of the bear, so when it is clear that they are supposed to leave the room, they do so willingly. Once the natives have left, the bear removes its head and Heyward sees that it is Hawkeye; Hawkeye explains that he stole the costume from the conjuror after knocking the man out, which is why he has been able to have such freedom--everyone thinks he is the conjuror. He explains that he had to keep disrupting the fake ritual so the Hurons would not discover that Heyward was not really performing a healing ritual.
Soon Magua unexpectedly appears at a secret entrance to the cave. Hawkeye pretends he is the conjuror.
The mimic animal, which had advanced a little, retired slowly in his front, until it arrived again at the pass, when, rearing on his hinder legs, it beat the air with its paws, in the manner practiced by its brutal prototype.
"Fool!" exclaimed the chief, in Huron, "go play with the children and squaws; leave men to their wisdom."
Magua is unmoved by the bear because he believes it is the conjuror. It is a costly mistake, for Heyward and the bear (Hawkeye) are able to catch the conniving chief off guard and tie him up. The two men sneak Alice, the dying woman out of the cave.