The monster, of course, is Almachius. We first become aware of him when he decrees that everyone must worship at the shrine of Jupiter or die, but from the reader's point of view he's still a distant threat, since Valerian and Tiburtius's executions take place off-stage and we never see Almachius face-to-face. We get the feeling, though, that Cecilia's whole life has been preparation for the confrontation that's to come when she receives Almachius's summons.
Cecilia's dream stage actually comes before her call: the Christian life she leads prepares her to confront the monster. She is not fearful at all, for she knows that God will protect her, and that God will provide eternal life if she loses her life on earth.
When Cecilia finally comes face-to-face with the monster, she is unable to convert him as she has all other non-Christians because of some moral failing within him. Instead of ending victoriously, it appears that Cecilia's battle will be a losing one. After all, Almachius does seem pretty powerful. And isn't it true, as he says, that he can sentence Cecilia to death?
The torturous death Almachius has devised for Cecilia fails to kill her, but Almachius has other methods. When he sends his executioner onto the scene to dispatch Cecilia with a sword, it looks like time may be running out for our heroine.
Cecilia not only survives being boiled alive in a cauldron, but also three strokes of the executioner's sword. Then, she remains alive for three days while her head's basically dangling from her body. If that's not a thrilling escape from death, we don't know what is. Cecilia's failure to die 'kills' Almachius because it reveals his claims to power as hollow: Cecilia will die when God is good and ready for her to die, because God is the only truly powerful being in this story. And although Cecilia dies in the end, she goes to heaven to live on eternally. Plus, her house is made into a church, ensuring that her legacy will continue through the people who worship there.