"The Tell-Tale Heart" by Edgar Allan Poe is a short story written from the first person point of view of an unreliable narrator. As the story progresses, we find out that the narrator is not just unreliable, but actually insane. In the story, we have two overt conflicts, and an implied one that is really central to our reading experience.
The first overt conflict is between the narrator and the old man, or more precisely the old man's "evil eye", as the narrator claims he had no actual issue with the man himself but only with the eye.
The second conflict is between the narrator and the police, with the narrator striving to conceal his murder of the old man and the police trying to discover what happened.
Perhaps the most interesting conflict in the story is the one between the narrator and the audience, with the narrator striving to convince the audience that he is sane, but with every sentence increasingly inadvertently revealing evidence of his insanity.