While it can best be argued that Shakespeare's Hamlet from Hamlet and Jimmy in Look Back in Anger are mostly unlike each other--particularly since Hamlet dies a tragic death and Jimmy doesn't--there are points that can be found that may be viewed as making Jimmy a Hamlet-like figure. The first is that both young men are motivated psychologically be their fathers' deaths. Jimmy's father died when Jimmy was ten. He had spent six months sitting by his father to keep him company while his father slowly died. Hamlet came home from abroad to find his father had been murdered.
Hamlet puts off taking action in the play because he debates existential questions with himself as he philosophizes and examines the rightness and wrongness of taking action in revenge and taking action on the say-so of a ghost who might be a demonic captive of Hell. Jimmy focuses on existential questions as they exist for young men in the mid-section of the twentieth century. In addition, both Hamlet and Jimmy are psychologically disturbed men who aren't wholly the masters of their emotions. Hamlet is melancholy and temperamental as with Ophelia while Jimmy is angry, judgmental, and abusive as with Alison.
An important difference between Hamlet and Jimmy that makes them unlike each other is that whereas Hamlet can't choose a course and act upon it, Jimmy has no trouble choosing courses and acting. Another difference is that whereas hamlet lacks personal fortitude, which keeps him from taking action, Jimmy consistently displays personal fortitude as when he "threw down the gauntlet" to Alison causing her to marry him.