First, the prompt is somewhat confusing as the main issue in Shakespeare's Hamlet is not the protagonist's reluctance to accept reality, but his reluctance to act upon it.
The first incident you should discuss is his encounter with the ghost. In Shakespeare's period, supernatural apparitions were associated with the devil, and thus Hamlet and his friends are understandably concerned about talking with and following the advice of the ghost. The tragic consequences of doubting the ghost would be letting the murder of his father go unavenged.
Hamlet's reluctance to kill Claudius when he is at prayer can be said to lead directly to Hamlet's own death. Had Hamlet killed Claudius earlier in the play, at the first opportunity, he would have survived rather than died at the end of the play.
Hamlet's delay in killing Claudius, and elaborate scheme of feigning madness and rejecting Ophelia, leads to the tragic consequence of Ophelia's suicide. Again, had Hamlet simply accepted the necessity of killing Claudius and done it, Ophelia would have lived.