First of all, Hamlet himself questions whether it is to be or not to be. In Act three, Scene one, Hamlet questions which act is more noble. Is it more noble to suffer from wrong deeds that one has done unto one or is it more noble to end the suffering by fighting? In this soliloquy, it is clear that Hamlet is torn between what is more noble:
To be, or not to be, that is the question.
Is it nobler in the mind to suffer
The slings and arrows of outrageous fortune
Or to fight against a sea of troubles,
And end them by fighting?
Hamlet has questions that are unanswered. He is not able to really think straight at the moment. Should he murder Claudius or not?
If I were to write an essay on Hamlet's indecisiveness, I would point out that it is not easy to murder someone. Unless you have killer instincts, it is difficult to murder someone. Only evil people sit around and premeditate someone's murder. It is not a natural instinct to murder someone in cold blood. Clearly, Hamlet is seeking the more noble act.
The next point I would make would be that Hamlet is not certain that his Uncle Claudius has murdered his father. Imagine, who could do such a thing? Again, murdering someone goes against natural instincts. How could Hamlet's Uncle Claudius kill his own brother. That goes against the goodness of nature and the bonds of brotherhood. Hamlet must be certain of Claudius' guilt before he can make a decision to retaliate.
When Hamlet learned for certain of his Uncle's guilt, again, murder does not come natural to Hamlet. He also is not sure how to go about the murder. Hamlet desires to avenge his father's death, but the exactness of the murder is unclear to Hamlet. One could die while murdering another. Hamlet must take into consideration that he could die while trying to murder Claudius. Clearly, Hamlet is stressed over his own father's murder, but he has to plan the right way to murder his Uncle Claudius. At one point, he thought he had murdered Claudius but it turned out to be Polonius. This murder only complicated things for Hamlet because of his love for Ophelia.
Again, murdering someone does not come natural to most people. Also, Hamlet had to be certain of Claudius' guilt, and lastly, Hamlet has to find the perfect plan and perfect time to murder Claudius. He does not desire to die in the process.
In the end, Hamlet found the perfect time and perfect way to kill Claudius. Of course, it happens as Hamlet the hero is dying himself:
But Hamlet is far more than an outstanding example of the revenge play. It is, to begin, a tragedy in which the attainment of justice entails the avenging hero's death.
Knowing that one may die in avenging his father's death is a good reason to be indecisive about murdering another. In other words, it is not easy to plan to kill someone when you know that there is a chance you may die in the process.