In this stage, we see the setup of who loves whom: Esmeralda wants Phœbus, Frollo wants Esmeralda, Quasimodo just wants somebody. So now we have a sense of what all the drama is going to be about. On a side note: we can't really trace a single "hero" in this novel, so instead, we're going to show how the three main characters—Esmeralda, Frollo, and Quasimodo—collectively follow the pattern for tragedy.
In the Dream Stage, we move from characters wanting things to characters doing things related to their desires. In this section, Esmeralda gives Quasimodo water while he's at the pillory, which is an act of kindness that causes him to love her. Esmeralda, on her end, meets and sets up an encounter with Phœbus. The final character whose "dream" is fulfilled is Frollo, who "catches" Esmeralda by stabbing Phœbus (and steals a kiss from her while he's at it). This stage starts somewhere around the chapter "A Tear for a Drop of Water" (Book VI.IV) and lasts until the end of Book VII.
Things definitely get "frustrating" for poor Esmeralda in this stage: she is imprisoned, tortured, accused of murder, and sentenced to death. On top of that, she's frustrated in her desire when she is told that Phœbus is dead. Frollo seems to have got what he asked for... until his desire to see Esmeralda hanged is frustrated when Quasimodo rescues her and proclaims sanctuary. That makes Book VIII the Frustration Stage.
It's easy to identify when the Nightmare Stage begins, because Frollo literally has feverish nightmare visions in the chapter "A High Fever" (Book IX.I). This section ends up being a nightmare for Esmeralda, too. Although she has escaped the gallows for now, she's locked in Notre-Dame with a priest who wants to rape her (and tries to, at the end of Book IX). Poor Quasimodo also realizes that there is no hope that Esmeralda will love anybody else but handsome Phœbus. You could say that things are literally "closing in" on these characters as the mob of Tramps approaches Notre-Dame.
Destruction or Death Wish Stage
As the mob attacks, all of the characters are forced to act. Quasimodo has to defend the cathedral, Frollo has to steal Esmeralda before the mob gets in, Esmeralda has to not get caught by the mob that wants to either rescue her or kill her (no one is really sure which it is). She also has to avoid the priest who is also trying to kill her. The book ends, of course, with the destruction of all three of our heroes.
Sufferers of the Hero's Recklessness
The Rival or "Shadow": Phœbus. He's the rival of everyone vying for Esmeralda's love, and even though things turn out comparatively well for him, he still ends up getting stabbed.
The Innocent Young Girl: Definitely Esmeralda. She fits all of the three criteria for Innocent Young Girl, and she suffers for the lustful actions of Frollo.
Other characters who end up suffering because of the hero's (mostly Frollo's) actions are Jehan du Moulin, who ends up killed by Quasimodo during the attack on Notre-Dame, and the Sack Woman, who reunites with her daughter only to end up dead. What a downer.