First, it is commonly believed that Hamlet distrusts pretty much everyone in the play (with the exception of his old schoolfriend Horatio). The following characters are the most prominent recipients of Hamlet's distrust: Gertrude (his mother), Ophelia (his girlfriend), Polonius (his girlfriend's father and the right-hand man to the new King) and Claudius (his uncle and the new King of Denmark). Explain what degree of distrust Hamlet exhibits toward each (mild, medium or intense) and then for each one explain why he distrusts this person. This is from the perspective of the early parts of the play - NOT from what he'll find out later. Keep your explanation from the point of view of first two acts (even if you've read the entire thing).
Second, how can an individual grow bitter, angry, and distrustful of people and their society, as Hamlet has become? What's behind this?
Clearly these people don't start their life this way. What leads to it? How can trying to hold true to your individuality and not conform connect to this? Consider this. Feel free to note aspects of Hamlet's life/situation to make your point or consider situations you might know of personally.