In Act II Scene 2 of Hamlet in the passage beginning "is it not monstrous..." which is not included in the passage: litotes, alliteration,...

There are no examples of chiasmus (reversing the order of words in identical phrases) in Hamlet's soliloquy at the end of Act II, Scene 2. There is an example of chiasmus earlier in the scene, when Polonius says:

That we find out the cause of this effect
Or rather say, the cause of this defect,
For this effect defective comes by cause.

In fact, Polonius is much given to the use of chiasmus, which can lead to rather bloated, long-winded, bombastic speeches throughout the play. But Shakespeare does not use this device in Hamlet's speech. As for the other devices mentioned in the question, one example of litotes in Hamlet's soliloquy is "for it cannot be/But I am pigeon-liver'd and lack gall." We see alliteration in "...by the very cunning of the scene/Been struck so to the soul..." Finally, Hamlet uses metaphorical language when he calls himself a "scullion," an "ass," and the King a "slave." So the only choice not included in the soliloquy is chiasmus.