Charon was assigned to ferry over the River Styx the souls of the deceased who had received the rites of burial.
During the Twelve Labors of Hercules, when he was sent to capture and take Cerberus from Hades, Hercules forced Charon to take him there. After that, Pluto punished him for letting Hercules into the Underworld by keeping him in chains for a whole year. Charon has harbored a dislike towards Hercules ever since.
When Hades stole the Shield of Minerva and turned the Agents of S.M.A.S.H. to stone, the Hulk and Hercules journeyed to the Underworld to put a stop to his plans and turn their friends back to normal. Therefore they needed Charon to take them across the river but refused to take any living, as Hercules attempts to sway him failed, he knocked him into the river to steal his raft but came back up to stand his ground against them. Hulk reasoned with the Ferryman that they needed to stop Hades at all cost, witnessing his act of heroism and selflessness for others, Charon made an exception to take them across.
When Hulk and Hercules fell into the River Styx from their fight with Hades, Charon rescued them onto his raft for not wanting someone as courage as Hulk to fall by Hades' hands yet could not say the same for Hercules. He then gives them a ride back to the surface.