For a three-act plot analysis, put on your screenwriter’s hat. Moviemakers know the formula well: at the end of Act One, the main character is drawn in completely to a conflict. During Act Two, she is farthest away from her goals. At the end of Act Three, the story is resolved.
Act I
In the first act of the novel, the priest alternates between fleeing from the police and ministering to the remaining Catholics who desire his services. The lieutenant keeps on his trail. The mestizo bides his time for the right moment to betray the priest for a reward. This action ends when the priest follows the mestizo certain that he'll be captured by the lieutenant.
Act II
The priest tries to talk the dying American criminal into making a confession, but fails. He's subsequently captured by the lieutenant, taken to prison, and brought before the firing squad. Another one bites the dust.
Act III
With the last priest now dead, the lieutenant's plan seems to have worked, but unbeknownst to him, a new priest arrives in the capital.