The Hero in Greek Mythology overcomes great obstacles, natural phenomena and supernatural creatures, eventually achieving a near godly status by challenging and trying to exceed his own humanity. Other than the mountain referencing Sisyphus and Prometheus, Homer's Odyssey is another reference point, as Poi fights monsters, resists temptation, and spends his life becoming worthy of the peach. A shot of him sailing across a sea of peaches is the main reference to this.
To Poi, reaching the peach means accomplishing his life goal. He doesn’t take it in the beginning, because he overthinks his approach, he only feels ready for it at the end, having endured and overcome all obstacles. The trials, montaged to show a long passage of time, represent him becoming this hero.
The Hero's Quest, Adventures and Video Games
The story uses a traditional adventure narrative, where the hero overcomes obstacles in order to reach the prize. The different locations and variety of trials also refer to levels of a video game, where the protagonist’s goal is always just one step ahead of them: Mario’s Princess Peach (!) is always in another castle. This shows that Poi sees getting the peach as the climactic moment of his life, only to have it be just an average fruit. The use of this genre serves to makes his prize all the more underwhelming and meaningless.