I regard the narrator, Montresor, as unreliable because he very much wants his auditor to think his crime is somehow justified. He seems to be speaking to a member of the clergy, and he is probably on his deathbed making his last confession. He initially claims that his audience "so well know[s] the nature of [his] soul," and, in the last lines, he says that it has been "half of a century" since he committed this crime, so he is clearly now an old man. After keeping his secret for so long, why would he now tell unless he urgently needs to clear his conscience?
Montresor begins the story with an overstatement when he says, "The thousand injuries of Fortunato I had borne as I best could; but when he ventured upon insult, I vowed revenge." It is unlikely that Fortunato had injured Montresor a "thousand" times, but it is notable that Montresor feels that he had. He seems to be trying to build his case, so to speak, against Fortunato so that the murder seems more defensible. Thus, Montresor has strong motive to influence his audience, a priest, to agree with him that Fortunato was a bad person and so, in some way, deserved what he got. Montresor's motives to inflate Fortunato's bad qualities render him unreliable.