In the scene where Indiana Jones had found where the Ark of the Covenant was located, and him and some friends went there and they realized the bottom of the pit was covered with snakes. Jones might not fear a lot of things but a snake was his biggest fear. For him to be a man and admit to his fear of snakes and overcome his fear is a sign of an epic hero.
He showed intelligence and self-confidenc throughout the movie by being able to find out where the treasures were hidden before the Nazis were could even think about looking.