Do you think Montresor achieves the kind of revenge he says he wanted at the beginning of the story?
I'd say yes and NO, and this is why:
At the beginning Montresor says, "I must not only punish, but punish with impunity. A wrong is unredressed when retribution overtakes its redresser. It is equally unredressed when the avenger fails to make himself felt as such to him who has done the wrong."
By this he means that he doesn't only want to punish and get away with it, he wants to correct a wong done to him. Settling for vengence is not enough. He wants Fortunato to understand why he is being punished and to plead for forgiveness/mercy. He wants Fortunato to realize that Montresor, the man whom he has insulted time and time again, is the superior man.
Montressor does get part of his revenge. He kills Fortunato and gets away with it. But his revenge is incomplete. Just before the last brick is placed, Montressor has been taunting Fortunato, trying to make him plead or scream--that would be satisfaction. Instead, Fortunato remains silent. At this Montresor says, "I thrust a torch through the remaining aperture and let it fall within. There came forth in return only a jingling of the bells. My heart grew sick - on account of the dampness of the catacombs."
Montresor tries to excuse his heart sickness by blaming it on dampness, but the dampness had not bothered him before. His real sickness came from the realiazation that his revenge was incomplete. He did not get the reaction from Fortunato that he craved.