I am reading Hamlet and was curious if there is "evil" revealed in the characters of the play.I am trying to find the evil in the characters such...

Concerning Shakespeare's Hamlet,
you're looking at the wrong character if you're looking at Hamlet for the presence of
evil.

Hamlet's killing of Polonius is a mistake.  He thinks
it's the king behind the arras when he kills
Polonius:

I
took thee for thy better.  (Act
3.4.32)

Hamlet can be accused
of cruelty in his treatment of Ophelia and Resencrantz and Guildenstern, but not evil. 
His treatment of those he hurts is the natural result of the wrongs they do him, as
least in part.  If he errs, it is in his going too far.

If
you want evil, examine Claudius.  He kills his brother, a sin on a level with Cain
killing Abel, then marries his brother's wife, which is seen as incest in his society. 
Once he knows Hamlet knows about his murder of King Hamlet, he arranges for Hamlet's
execution in England.  When that fails, he plots to underhandedly kill Hamlet by
unblunted sword and poison.

Finally, Claudius knows his
actions are evil and he knows he is eternally damned, but he still refuses to give up
his ill begotten gains, so to speak.  He would like to be forgiven, but he is unwilling
to give up what his sins helped him achieve.  As he says while
praying:

O,
what form of prayer

Can serve my turn?  'Forgive me my foul
murder'?

That cannot be, since I am still
possessed

Of those effects for which I did the
murder--

My crown, mine own ambition, and my
queen.

May one be pardoned and retain th' offence?  (Act
3.3.51-56)

If you're looking
for evil, Claudius is your man.