Disagree. Hamlet knew his duty very well and does his best to fulfill it--until it conflicts with his morality.
He knows he must do what his father asks; when it conflicts with his own morality, he is torn. He considers suicide more than once because he is caught between these two things
He knows he must try to shield Ophelia, whom he loves, from the coming troubles; this conflicts with his love for her, yet he does it. The moral issues return in the form of remorse when he discovers her fate.
He knows he must be obedient to his mother; fortunately, she doesn't ask much of him. The Ghost, however, has asked him to treat her with continued respect, which conflicts with his wish to seek his revenge against her, as well.
He even knows he needs to obey the wishes of the King when he asks him to stay and not go back to school; he is torn because he hasn't spoken with the Ghost yet and simply wants to leave this "prison" called Denmark.
These are all duties Hamlet did not shirk. He does experience remorse; however, not all of it is because he neglected to fulfill his duties.
Hamlet seems to be a melancholic perfectionist. (Will this term make the psychology magazines?) When conditions are not optimum for his action which he delays because of his depressive personality, he rationalizes that it is not the appropriate time because he cannot be sure that the ghost is truly his father's, Claudius will go to heaven if he kills him while he prays, is it better to just die and fight the "slings, and arrows," etc. etc.
Finally, after eliminating his mother because of her "incestuous love" and betrayal of his father's love, Rosencrantz and Guildenstern because they considered betraying him, Ophelia because she is not pure and has allowed her father to have her talk with him, Laertes because of his quarrel over the death of Polonius, Hamlet finally measures himself against Fortinbras who willingly goes into battle "for an eggshell" of a reason compared to his and feels remorse for his delay. Only then does he declare himself "Hamlet the Dane" and so battle.
If by his duty you mean to avenge his father's murder, you must understand the world in which Hamlet lived. Hamlet lived in a Roman Catholic world. "Vengeance is mine sayth the Lord." To kill Claudius would be a mortal sin and condemn him to eternal damnation.
If his duty is to kill Claudius, he is caught between doing his duty or another option is suicide. Either way he will suffer eternal damnation. This would cause anyone to hesitate.
He also hesitates since he was given the information by a ghost who looked like his father. Can he be sure it is his father? Could it not be the devil who has taken on the disguise of his father?
Hamlet's problem is how to accomplish his objective without losing his soul in the process. Unlike Romeo who does not check out his information before he acts, Hamlet examines his problem from every possible angle.
He has the perfect opportunity to kill Claudius while he is praying. Unfortunately if one dies while praying, it was believed the soul would go directly to heaven which is something Hamlet does not want for Claudius. What Hamlet does not know is that his uncle cannot pray due to his guilt.
Many people die in the play either directly or indirectly due to Hamlet's actions and inactions yet he is able to accomplish his objective. What happens to his soul is anybody's guess.
His intense remorse, as you call it, is the result of his father's death, his mother's remarriage to a man he doesn't trust or respect, his feeling of isolation, his moral and ethical situation, and more.
To really understand Hamlet and the play, it is necessary to understand the world of the play. The days of "frontier justice" had been replaced by the moral world created by the Roman Catholic church. Shirk his duty? I don't think so.
I am going to have to disagree with this statement. I think it would be more accurate to say that Hamlet knew what his father's GHOST told hiim was his duty -- to get revenge for his father's murder by Claudius. Hamlet did fail to accomplish this, although he made many attempts. His failure did cause him the most intense remorse, but that remorse was understandable. Why? Because the ghost wanted Hamlet to kill a king. Killing was bad enough, but killing a king was considered a particularly odious deed in Elizabethan times (note this theme in Macbeth). In fact, Hamlet believes at times in the play that it would be easier to kill himself than Claudius.
Hamlet has several chances to kill Claudius, but he hesitates. One time it is because Claudius is praying and Hamlet concludes that if he killed Claudius then, he would no doubt send him straight to heaven, since he is praying. Even at the end when Claudius dies, it is as a result of his own doing, not Hamlet's. And Hamlet dies himself.
So, while Hamlet knew what his father's ghost wanted him to do, he had a conscience and he was conflicted over what really was the right thing to do. Should he do what his father told him to do and what he wanted to do, or should he do what God would have wanted him to do, leave vengeance to God.
I think others will disagree, but this is my view. It is no easy thing to be given instructions to kill someone, even if the person deserves it. And if one believes in the Divine, as Hamlet indicates that he does, this is a very serious sin, even when the person is as evil as Claudius. "An eye for an eye, a tooth for a tooth," is not so easy to carry out.