There's no great mystique about an "academic writing style". The most important thing is to keep your writing clear and concise and make sure that you get your ideas over in a comprehensible form. It's clear expression of these ideas that will impress your tutor, not a string of long, inappropriate words found in your dictionary. A wide range of vocabulary is of course important, but you must use the right word, and shorter ones are often better than longer ones.
The most important thing to remember is generally to try to avoid everyday, informal language, especially colloquial expressions and slang. Also, spoken language is naturally full of hesitations, repetitions, grammatical errors and unfinished ideas. In your writing, however, structure is much more important: sentences should be complete and ideas arranged into paragraphs or sections, and you should aim for perfection in your grammar and spelling. However, especially if English is not your first language, don't become too obsessed with this, to the point perhaps of copying word for word from your sources. What’s important is that you clearly show your understanding of the subject and your ability to manipulate information to answer a specific question or complete a specific task, and as long as any grammar errors you make don’t impede this, then it shouldn’t be a problem.