In this passage, Gertrude is addressing Hamlet. He is in her room and has been berating her for marrying Claudius. He is in a frenzied state and suddenly sees the ghost appear. Gertrude can't see it, so she is questioning her son about what is going on. Some literary devices used are the following.
First, she uses alliteration, which is when words beginning with the same consonant are put close together. An example is the repeated "st" sound when Gertrude says that Hamlet's hair
Starts up and stands on end.
Gertrude uses simile, a comparison employing the words like or as , when she compares Hamlet's hair standing on end to sleeping soldiers who hear an alarm. She uses a simile again when she compares his hair to "bedded excrements," by which she means that it is standing up like spikes or horns all over...
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his head, indicating that he is frightened. "Excrement" means anything that comes out of the body, which is where we get our current understanding of the word.
Gertrude advising Hamlet to "sprinkle cool patience" on his flaming distemper is a metaphor, a comparison that does not use the words like or as. Gertrude is comparing patience to water, which you would sprinkle on a fire to lessen it.
The words "alas" and "O" are exclamations. They carry little meaning, but they convey the strong emotions that Gertrude is experiencing.
Finally, as it must, the passage uses imagery, or description using any of the five senses of sight, sound, touch, taste, and smell. Gertrude needs to convey to the audience that she does not see the ghost that is so frightening Hamlet. She does so by saying she is seeing only "incorporal air," while his eyes are popping out of his head wildly at what he sees.
Hamlet is berating Gertrude for marrying her husband's murderer. When she can bear it no longer, the ghost (Hamlet's father/Gertrude's previous husband) appears and speaks to Hamlet, asking him to calm Gertrude down and go easy on her. For whatever reason, Gertrude cannot see the ghost, so she thinks Hamlet is mad. In these lines, she questions Hamlet's sanity.
When she asks how he can hold discourse with "incorporal" air, she is asking why he is talking to nothing. "Incorporal" (incorporeal is the modern spelling) means having no mass or no material existence. The "corp" comes from "corpus," which is Latin for "body." This is a stretch, but you can argue that this is an example of apophasis. This is a device wherein the speaker mentions something by denying it or by denying it should be addressed at all. When Gertrude uses "incorporal" (containing the root "corpus" or "body"), she is making a subtle reference to someone that Hamlet is speaking to or some "body" that she can not see. It is just an interesting word choice in that it refers to a body that Hamlet can see but she can not or will not.
The personified "spirits" peeping through Hamlet's eyes and the simile comparing his hairs to awakening soldiers creates some interesting imagery. Here is another subtle allusion to a spirit or ghost speaking with Hamlet. In these lines, Gertrude uses an adjective (incorporal) and a metaphor (spirits) that allude to "body" and "spirit" respectively. There is a bit of dramatic irony here: the audience will see the connection to Hamlet's father's dead body and current ghost but Gertrude does not. The imagery of the soldiers adds to Gertrude's impression of Hamlet as a crazy person ready to commit violence.