This idiom is about an unpleasant surprise in a confrontation, someone thought to be easy to handle turns out to be much tougher instead. Let's test each option against that sense:
- To trap a wanted criminal with great difficulty: This describes an actual difficult capture of a criminal, a literal law-enforcement scenario, not the figurative sense of being outmatched by an opponent.
- To catch a dangerous person: This is close in flavour, mentioning danger, but it still reads as a literal act of catching someone, rather than the figurative idea of getting into a situation with someone tougher than expected.
- To meet with disaster: This is too broad and generic, the idiom is specifically about an opponent or adversary, not misfortune in general.
- To deal with a person who is more than one's match: This exactly captures the figurative meaning, expecting an easy opponent and instead finding somebody stronger or more capable.
The first two options read the idiom too literally around "catching" someone, and the third loses the "opponent" sense entirely, leaving only the option that captures the figurative meaning of encountering an unexpectedly tough adversary.
Therefore, the correct answer is To deal with a person who is more than one's match.