Initiation
Now the hero has entered the unknown world. The hero takes part in various adventures during Initiation. There are six stages that may be present in this part of the journey. The hero gains knowledge and power along the way, eventually acquiring the ultimate boon.
Road of Trials
The hero is subject to a series of tests. He must pass a succession of ordeals in the unknown world. These tasks may be completed alone or with help. The hero tends to be successful at the beginning, before failing a trial or two. Every task adds to the hero's knowledge and experience.
Meeting with the Goddess
At some point, the hero experiences a powerful love that parallels the love an infant feels for its mother. This is often represented by the hero meeting his true love.
Woman as Temptress
Of course, there are always temptations that might cause the hero to stray from his quest. Woman is used as a metaphor for the physical/material temptations that distract the hero from continuing on his spiritual journey. The temptation does not have to be a woman or even a person.
Atonement with the Father
This is the middle of the journey. The hero must be initiated by whoever or whatever holds the ultimate power in this new world. In many stories, it is a fatherly figure who has incredible power. Once again, it does not have to be a male, just the person or thing with the ultimate power.
Apotheosis (I had trouble understanding this one at first)
In this stage, the hero typically "dies" in some way. This can be a physical death or a spiritual death. The hero is able to achieve a state of enlightenment because of this death. It is also the period of rest before the hero begins Return. The best example I can think of from the Harry Potter series is the King's Cross chapter in Deathly Hallows.
Ultimate Boon
The ultimate boon is the goal of the quest. All the other steps were to prepare the hero to be able to handle the ultimate boon. The ultimate boon usually brings immortality, such as the Fountain of Youth or the Elixir of Life. It can also be a widely coveted item, like the Holy Grail.
Once Harry steps foot into Hogwarts, he experiences his first test: The Sorting Hat! He is generally successful early on in his road of trials. A memorable moment is during the first flying lesson, where both Harry and Draco Malfoy disobey Madam Hooch and fly when she takes Neville Longbottom to the hospital wing. Professor McGonagall happens to see them flying and Harry believes he would be severely punished. Instead, she takes him to see the captain of the Gryffindor Quidditch team and Harry becomes the new seeker. There is also the fight with the troll in the girl's bathroom, where Harry gains the valuable friendship of Hermione Granger with the help of Ron Weasley. Of course, Harry is not always successful, especially in Professor Snape's Potions classes.
Now, this one may seem like a stretch (but give me points for creativity because I will for you!). For Harry, the meeting with the goddess occurs when Harry first finds the Mirror of Erised. This is the first time Harry sees his mother and father and his family in the Wizarding World. (Lily Potter also looks quite similar to Ginny Weasley, who is Harry's true love at the end of the series.)
The Mirror of Erised acts as the woman as temptress, since Harry continues to visit it many nights in a row. He almost forgets about his quest.
What brings Harry back is the atonement with the father. Albus Dumbledore reveals how the mirror works and warns him about getting lost in the Mirror of Erised. He tells Harry the mirror will be moved, so Harry should go back and focus on his schoolwork.
Apotheosis occurs when Harry drinks the potion and walks through the fire (with black flames). Now he is truly alone since all his helpers have been left behind; Ron sacrificed himself during the chess game and Hermione has to go back to get Ron. This is also when Harry realizes Professor Quirrell is the real enemy, not Professor Snape. He must figure out how to get to the Stone before Quirrell.
Harry does get the Philosopher's Stone from the Mirror of Erised. He wanted to find the Stone and not use it. The Philosopher's Stone is the ultimate boon. It creates the Elixir of Life, which many want, especially Lord Voldemort.