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.
Here are a few general points to remember when you are writing your assignments. As well as using appropriate language and aiming for 100% accuracy in your grammar and vocabulary, you should also remember that you're writing for someone else, and hence the importance of punctuation, sentences, paragraphs and overall structure, all of which help the reader.