The "monster" is the threat of becoming a "clockwork orange" – an extremely visceral threat that Alex faces as a result of having undergone Ludovico's Technique. After all, a man who is unable to exercise freedom of choice ceases to be a man – and Alex is trying to rebel against the monstrosity of it.
Interestingly enough, this Basic Plot of Booker’s does not apply until Part Two of the book, meaning that Part One mostly provides background and buildup for the ordeal to come. Nonetheless, the "monster" has been anticipated in part one; for instance, when Alex reads from F. Alexander's loose manuscript entitled A Clockwork Orange. Most of part two has Alex set up to embody the highly feared "monster." In any case, it is definitely something that everyone (except the State, we suppose) fights against, and so is an appropriate "monster."
Alex hooks up with F. Alexander, whose plans of overthrowing the Government are already underway.
Beaten up by his former droogs and left to die, Alex wanders toward a house at the edge of a suburb. F. Alexander takes Alex into his home, feeds him, and gives him a place to rest and recuperate.
Unfortunately, F. Alexander recognizes Alex as the rapist and murderer of his wife, arousing within him a thirst for vengeance against Alex, in addition to a desire to use Alex as a pawn against the Government.
Of course, just when things are going well, complications are bound to arise. In this stage, just as Alex prepares to sign the confession/article F. Alexander has drafted for him as part of their shared subversive plans, F. Alexander realizes that he has unfinished business (personal, of course) with Alex. Thus, instead of executing the original plan (i.e., publish something that makes the Government look irredeemably evil), he comes up with a new plan.
Cornered by the classical music blasting through the wall of his locked quarters, Alex leaps from the multi-storied building, perhaps to his death.
The new plan by F. Alexander and his associates is the nightmare that Alex must confront. Unable to endure the pain of classical music as acquired through his associative learning treatment, Alex has no choice but to leap from a tall building to escape.
Thrilling Escape from Death and Death of the Monster
Luckily, Alex does not die, and the circumstances lead to the State's reversal of Ludovico's Technique on Alex, restoring him back to his old self.
Alex doesn't die from the jump and instead enjoys a few weeks of being an invalid in bed. His nightmarish journey gains public attention, and the State's doctors work to restore him in an effort to please the public and gain votes for the upcoming election. A clockwork orange no more, Alex is turned back into the evil urchin that delights in violence. The icing on the cake is that F. Alexander has been jailed.