The Hero's Journey is a framework that scholar Joseph Campbell came up with that many myths and stories follow. Many storytellers and story-readers find it a useful way to look at tale. (That's actually putting it lightly. Some people are straight-up obsessed.) Chris Vogler adapted Campbell's 17 stages of a hero's journey, which many screenwriters use while making movies. Vogler condensed Campbell's 17 stages down to 12, which is what we're using. Check out a general explanation of the 12 stages.
"The Judgment of Paris" doesn't fit perfectly into the Hero's Journey structure, but we're giving it a shot. As the gross old saying goes, there's more than one way to skin a cat.
The ordinary world for Paris is chillin' in the pastures with his flock of sheep. It's nice.
Call to Adventure
The call to adventure sounds loud and clear when Hera, Athena, and Aphrodite, show up, get naked, and demand that Paris choose which of them is the most beautiful.
Refusal of the Call
There's no refusal at all for Paris. This is one adventure he doesn't mind taking on.
Meeting the Mentor
There's not really a mentor figure either, unless you count the goddesses themselves who encourage him with their divine beauty and... well... nudity.
Crossing the Threshold
Paris grips the golden apple in his hand and prepares to make his fateful decision.
Tests, Allies, Enemies
As each goddesses parades herself before him, Paris listens to the various bribes and tries to make his decision. Which offer will make his life awesome? Which will make it totally sucky? Hera offers him power. Athena offers skill. And Aphrodite...
Approach to the Inmost Cave
When Aphrodite offers Paris the hand of Helen, the most beautiful woman in the world, he just can't resist. Little does he know he's approaching a some seriously challenging times.
Normally, this section would be a little more overtly dramatic. Instead, Paris shows up in Sparta while Helen's husband, Menelaus, isn't home and makes off with the most beautiful women in the world.
Paris's reward is the love of the gorgeous Helen, whom he cherishes above everything else.
The Road Back
The Trojan prince heads back to his hometown of Troy to live happily ever after with his new lady.
The story definitely veers from the pattern from here on out. Paris doesn't rise again from the dangers of the Trojan War launched by Helen's husband, Menelaus. Instead, the Trojan Prince ends up dying.
Return with the Elixir
Unfortunately for Paris, there's no elixir. He's dead as a doornail, so it'd be kind of hard to claim it. Instead, the Greek armies totally destroy Troy, and Menelaus reclaims Helen as his bride.