The struggle between Hamlet and Claudius is a fascinating one. Discuss this statement supporting your answer by reference to the play Hamlet.
Concerning your question about Shakespeare's Hamlet, I'm not a big fan of trying to prove something is or isn't fascinating. The word, to me, is one of those glittering generalities that means nothing, or at least means something different to everyone who uses it. It's extremely vague.
That said, it's your assignment so I'll try to help.
The "dual" between Hamlet and Claudius is a cat-and-mouse kind of dual. Claudius thinks he is the cat, at least early on, because he knows something Hamlet doesn't--that he is a conniving murderer. He assumes Hamlet is unsuspecting. And Claudius is a worthy adversary. Make no mistake, he is capable and intelligent and ruthless.
But in actuality, Hamlet is probably the cat in the cat-and-mouse game. Hamlet certainly thinks so anyway, as he demonstrates when he tells Claudius that the title of the "play within the play" is "The Mousetrap." Hamlet is the cat, and he's going to catch the mouse with the play.
This, indeed, though, might have been different if not for the Ghost giving Hamlet the knowledge he lacked. In other words, if the Ghost doesn't inform Hamlet of his death at the hands of Claudius, Claudius might have managed to maintain the position of cat to Hamlet's mouse, because Hamlet may have stayed unsuspecting. When the play opens, Hamlet is upset with and angry at Claudius for marrying his mother and for taking the throne that was rightly Hamlet's. But Hamlet in no way suspects Claudius of murdering old King Hamlet when the play opens.
This bit of knowledge would definitely have given Claudius the upper hand in the cat-and-mouse game with Hamlet. Thanks to the Ghost, though, Hamlet definitely turns out to play the role of cat in this predatory situation.