Ooooo! Let me try my hand at this! What a fun assignment for me! I think I'll take the first part of the soliloquy: 3.1.56-68). Here goes . . .
*sigh* What is the point of this life, anyway? Maybe we should all just kill ourselves. What's better, anyhow? Suffer here under the hand of fate? . . . or fight against that fate by taking our own lives? Ah, death, . . . it would end all of our heartaches. Damn, that's awesome. But, hmmmm, . . . what will happen AFTER death. Hmmm, . . . that's the real issue isn't it? It's the only thing that makes me hesitate. (And, oh, I'm good at hesitating.)
In Hamlet, the speech is usually called a soliloquy, but I think it's really a monologue. Ophelia is on stage, and not unnoticed. She is waiting with her father, who withdraws, to give back all of his lover letters. Knowing this, Hamlet may be delivering the speech to her. Maybe it's not so much about him.
Prince Charles did a rendition which is very humorous. He knows a thing or two about being a Prince, I think. He too was passed over for the crown and has had some "mommy" and "girlfriend" issues. Here's some lines from his (I don't think I can publish it all due to copyright issues).
"To Be Or Not To Be" by Prince Charles
Well, frankly, the problem as I see it
At this moment in time is whether I
Should just lie down under all this hassle
And let them walk all over me,
Or, whether I should just say, 'OK,
I get the message,' and do myself in.
The Prince's tone here is not poetic, like Hamlet in the play, although it is written in iambic pentameter. He is rather cheeky about the proposition of suicide, using "do myself in" as a euphemism.
I don't think the real Hamlet is contemplating suicide for himself (only in general), so if you write yours in similar fashion, you might want to specify this. Rather, Hamlet is only contemplating about the nature of death and suffering in general. And I definitely don't think he wants Ophelia to kill herself either.
Here's another section of the speech from Enotes' wonderful "Text and Translation" section:
To die, to sleep,
To sleep! Perhaps to dream. Yes, there's the catch,
For what dreams may come in that sleep of death,
When we have left this life on earth,
Must make us stop.
You can look at others online, but your main goal is to keep it simple and personal. Hit 10 syllables per line without sounding too sing-songy. Good luck...
To like, die, yeah?... or like, not die.
That's what I'm getting at, man.
Bleah, I can't continue, it is too horrible and ugly. Why change what is beyond improvement?