Analyze how Margaret Atwood uses details, imagery, diction, language, and syntax to explore an issue of your choosing, and explain how the issue contributes to the meaning of the work as a whole.

This is a big question, so it might be difficult to know where to start. I would recommend settling on an issue first and then breaking down your answer to address the various component parts of the question.
Atwood's The Handmaid's Tale is most often read as a feminist novella, so it might be easiest to choose as your issue the way in which women are treated and controlled in the society Atwood describes. This intersects with the question of government power over the individual and the issue of how the government seeks to control sexuality and childbirth. Choosing the latter as an example, let us look at how to analyze Atwood's exploration of this issue.
Details: Part of what makes this novella strong in general is that Atwood uses small details to make her world vivid. Early in the story, Atwood describes how the girls sleep in a gymnasium in which "the hoops for the basketball nets were still in place," a detail which serves to make the setting both extremely real—the reader can imagine such a gymnasium, and this makes the world of the story seem less far removed from our own. Atwood does the same thing in addressing the issue of sexuality and control: details such as the "single mattress" of the bed in which "nothing takes place . . . but sleep" plant the seeds in our understanding of what will later be elaborated upon. Similarly, the fact that there are "few mirrors," "as in a nunnery," is a detail that helps us to understand the way in which the women are viewed, especially when compared to a context we understand. As she listens to Rita and Cora discuss their options," Offred listens also to the sound of them "shelling peas," a detail which lends sensory depth to the scene and makes it real. Throughout the story, Atwood uses details to create a sense of reality even while outrageous dictates are discussed: the effect of this is to make her world more frightening because it seems closer to ours.
Imagery: The imagery Atwood uses to describe the "tourists from Japan" helps us to understand the lens through which she has been encouraged to view women and sexuality. These women are described as "like robins," suggesting gaudiness, and their high-heeled shoes are described as "like instruments of torture." The broader details of the description show that the women are not, in fact, dressed in a way that would look outlandish to us, but the imagery Offred uses indicates that, to her, they are now outside of her philosophy and that of her society. They "teeter," and their "hair is exposed in all its darkness and sexuality," helping us to understand the context of a world in which exposed hair is equated with a sexuality which is in itself sinister or "dark." Their lipstick is like "scrawls on the washroom wall," something which is crude and associated with baser impulses.
In terms of diction, language, and syntax, I would argue that it is difficult to separate these into discrete categories. Atwood's use of language includes the way in which she uses syntax to convey her points; meanwhile, diction means the type of language a writer chooses, such as "poetic diction" or "archaic diction." As such, it may be simpler to consider "language, syntax, and diction" as elements of the same issue for discussion.
In The Handmaid's Tale, the question of language itself, and its inherent power, is one of the issues Atwood is exploring. Linguistic choices that hark back to archaic diction but are, at the same time, new coinages, such as "the Unwomen," combine with a society in which names are "passed from bed to bed" like currency because the women live in a society in which their own names are "forbidden." These elements both revolve around the wider issue of power being exerted over the women who inhabit the society and who are categorized in different boxes according to how society has interpreted them.
Atwood's choice of language and syntax reflect the neo-Puritan society in which the women live, whereas the structure of the sentences and the authoritarian diction suggests that Offred is often repeating dictates she has heard. When she explains that "arousal and orgasm are no longer thought necessary; they would be a symptom of frivolity merely," we can see an example of this type of speech pattern. The voice is passive: Offred is repeating the views of the wider society, which is not named. The placement of the adjective "merely" at the end of the phrase lends the sentence a conservative and old-fashioned air. Just as the society seeks to recapture what it believes to be the mores of a previous time, it imposes linguistic choices and syntactical structure upon the inhabitants which also echo times long past.
These are just a few examples to help you interpret this question, but I hope they give some guidance as to how to get started.