To add to that which has been written on Ophelia:
She is truly an innocent in the political world of betrayal and deceit, and, because of her mad suicide, she is denied Christian burial although politics seems to overrule this judgment. A pathetic young woman, Ophelia is easily dominated by her father, Polonius, and destroyed by circumstances and Hamlet's alternating professions of love and disgust.
A character representative of the ideals of youth and innocence, Ophelia is destroyed by the political corruption of the Danish court:
And I of ladies most deject and wretched,/....Now see that noble and most sovereign reason/Like sweet bells jangled, out of time and harsh,/That unmatched form and feature of blown youth/Blasted with ecstasy. O, woe is me/T' have seen what I have seen, see what I see! (III,i,151-157)
Her unjust death illustrates how far the court has degenerated as it corrupts even the pure and innocent.
I'm not going to make the case for you, but I will suggest some likely characters.
First, of course, is Hamlet's father. He was murdered by Claudius.
Second is Ophelia, who is ill-treated by Hamlet, presumably distraught from her father's death and ultimately goes mad.
Beyond this, it is harder to make a completely clear argument about a character's death having been unjust. The others engage in at least some behavior that is questionable.
I suppose the third would have to be Laertes. He is innocent in terms of his own life path and -- although rash -- is only trying to avenge the deaths of his father and sister.
Hamlet's father died unjustly, Ophelia died unjustly, and Gertrude died unjustly.