Revising the way your ideas are expressed is not about dressing them up in more impressive-sounding language to fit in with some notion of academic style - if you try to do this, you will end up producing gobbledygook, since you won't know the proper way to use this kind of language. What you should be looking for when you revise are ways of expressing your ideas more naturally and with greater clarity.
To see revision as a means to achieving a more natural style may seem paradoxical, since you probably assume that your first draft represents your most natural way of expressing yourself. But this is to ignore the rhetorical situation of your essay, in which what seems "natural" to you as a writer will seem awkward, clumsy and unclear to your reader.
Finding the best way of expressing your ideas is really a matter of compromise between several potentially conflicting requirements. It is easy for academic writing to become excessively abstract, and so make it hard for a reader to form a mental picture of the topic. To counteract this tendency, you need to consider whether your writing could be made more forceful by using more verbs and reducing the number of passive constructions (you should never use the construction "it is said that", for example, since as well as being very weak it avoids the need for referencing). It is also worth thinking about you could express yourself with greater economy, perhaps by leaving more minor aspects of your argument to be filled in by the reader's inferences. Conveying your ideas in a shorter way can help the reader, because it makes it easier for them to carry your ideas in their head.
The attempt to write more concisely can seem to conflict with the need to provide cues for your reader, which from an inexperienced writer's point of view often appear somewhat repetitive and unnecessary. But it's almost impossible to give your reader too many cues, so the question you need to ask yourself is whether you've provided enough of these.