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 Titans' story 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. Here's how we've diced up the story:
In order to escape being swallowed whole by his power hungry father, Zeus is forced to hide out in a cave in Mount Aegeum, in Crete. In this sense, Zeus does begin his journey as part of the "ordinary world," if you really want to call being raised by nymphs ordinary. Unfortunately, Zeus himself is never ordinary, and he's never without knowledge of his heritage the way, say, Percy Jackson is at the opening of The Lightning Thief. Knowledge of his divinity sets Zeus apart a bit from the average world around him, making this step of the Journey a loose fit.
Facing down his father is Zeus' destiny; Gaia explains this before the young Olympian is even born and presumably someone tells Zeus what the future has in store for him while he's growing up. Essentially, he got the call to adventure when he was about five minutes old. Granted, he wasn't able to answer it right away, but he didn't let it go to voicemail either.
As far as we know, Zeus never shied away from his destiny. This step simply doesn't fit our story.
For this step to seem natural, we need to refer to the version of the story that depicts Zeus seeking aid from the Goddess of Wisdom, Metis. Metis, a goddess of cunning and good counsel, was the daughter of two of the original Titans, Oceanus, and Tethys. In versions of mythology other than Hesiod's, Metis provides Zeus with a potion that will force Cronus to spit out the other Olympians. Pretty sneaky.
Zeus leaves earth and confronts his father in Heaven. Enough said.
Armed with Metis' magic potion, Zeus confronts Cronus, the enemy, and forces him to throw up the other Olympians, the allies. Hopefully they all showered before the group hug. It's difficult here to pinpoint a real test, because in the vast majority of versions of the myth there's no real challenge when Zeus confronts Cronus. Based on the writing, we're forced to assume that Zeus simply walked up and said, "Hey, Dad, I know you think you swallowed me whole at birth but as it turns out you didn't, and now I'd like you to drink this potion and proceed to chuck up my brothers and sisters." We'll just have to pretend that there was a big struggle; maybe something like the poison wine drinking scene from The Princess Bride.
Zeus and the Olympians prepare for war against Cronus and the Titans. (Pretty self-explanatory.)
Ten years of bloody battle pass – none of which we actually get to hear about – and we arrive at the decade-old stalemate between the Titans and the Olympians. Neither army seems able to gain the upper hand.
Enter Gaia, bearing her awesome prophecy of winning. Hesiod more or less skips over this part of the story, but in later versions of the myth we're told that Zeus and the Olympians are forced to slay the monster Campe in order to free the Cyclopes and the Hecatonchires from prison. Campe is depicted as a half-woman-half-dragon with a scorpion's tale; we figure facing a monster like this counts as an "ordeal."
Unfortunately, we're again presented with no sense of urgency. The myths just say that Campe is slain and the prisoners are freed. We'll have to imagine the Zeus undergoes some sort of character-altering struggle in the process.
Zeus ends up with lightning bolts and three boulder-throwing giants each with one hundred arms. Best reward ever. According to Campbell, this step of the journey is filled with both celebration and a sense of fear, as danger still lurks. With lightning bolts and boulder throwing giants at hand we're guessing the Olympians skipped the "sense of fear" part.
Zeus and the Olympians return to Mount Olympus and resume battle.
Technically, this is the part of the story where the hero faces death – literal or metaphorical – for the last time and is transformed by the process. Zeus more or less skips this step and instead just beats the crap out of the Titans.
The Olympians imprison the Titans in Tartaros and Zeus claims the throne of the gods on Mount Olympus, bearing with him the lightning bolts that are a symbol of his new power and authority. Go Zeus!