In simple language, what are the differences between synchronic/diachronic analysis and syntagmatic/paradigmatic analysis? How can these theories...

Without going into the structural linguistic terminology (which can be confusing and dense), I will define these two sets of terms on a basic level:

In simple terms, adopting a diachronic approach for a movie means that one would examine how aspects of the piece change over time. For example, one could look at the ways in which the plot unfolds from beginning to end, or how certain characters develop over time. By contrast, a synchronic approach means that one would analyze small segments individually—either scenes, or elements of a character at a certain point in time.

An syntagmatic approach entails that we examine a group of visual cues, or how elements in a film are interrelated. To do this, one could analyze a costume, a specific camera shot, or even lighting, and see how that one choice creates meaning. Another way of seeing this is to ask yourself why the director (or producer, etc.) chose to utilize a specific camera angle or costume. A paradigmatic approach, on the other hand, would require that one analyzes how a particular element (costume, camera shot, lighting) works at a particular point in the movie to create meaning.

All of these approaches would work for the movie you mention, and countless others. I would encourage the student to focus on what is most interesting in the film to guide their analysis and develop an argument from that point (unless other parameters have already been put in place).