To begin, Sysiphus began his journey by withholding information from one of the most powerful gods, Esopus. He made a deal to reveal the secrets in exchange for water for the citadel of Corinth. This demonstrated the existential tenet of free will because Sysiphus was taking fate into his own hands for his people.
Secondly, Sisyphus kept Death in chains which meant that many people on Earth were not dying. This demonstrated the existential idea that all our actions have consequences and that our actions can make a lasting effect in our lives.
Another example was when Sisyphus asked Pluto for permission to return to Earth and chaste his wife for not giving him a proper burial. Once returned to Earth he practiced another existential tenet, existence precedes essence, with this second chance in life and finds that he does not want to return to the underworld, he wants to make meaning to the life he has left.
Unfortunately, he was caught by Pluto and returned to the underworld to await punishment.
Sisyphus was condemned to be pushing a rock all the way up the mountain to find it rolling back down. The repetitive motion of the pushing of the rock demonstrates that there is no change in life that has no meaning, and the rock symbolizes the absurd in life and how Sisyphus repeatedly tries to overcome it.
In the end, Sisyphus could be classified as a tragic hero who follows these existential traits.