1. Shorten your sentences
There's a tendency to write long convoluted sentences which almost always read better when divided into two (or more). Firstly, your writing sounds more confident when you make statements - the cat sat on the mat, for example, is a simple, straightforward statement. Secondly, it's hard for the reader to hold a very long sentence in their head. By the time they've got to the end they've forgotten the beginning.
2. Cut the qualifiers
Academic writing is often about weighing up conflicting statements and leaving any judgements to the conclusion so it's tempting to add lots of qualifiers - maybe, might, can also, sometimes, possibly, perhaps, in certain circumstances etc. All qualifiers weaken your writing, so they should be used sparingly.
3. Watch out for connecting words
Essays are about a series of ideas linked to follow an argument. Linking or connecting words are useful, but you don't need them at the beginning of every sentence as the ideas themselves should clearly link. Moreover, therefore, also, on the other hand, despite... I have read sentences that start with a series of linking words. Please - more is not better.
4. Use a dictionary
The English language is a wonderful thing, crammed with a variety of wonderful words. Students often use good words, but not necessarily in exactly the right circumstances. Do you really know the meaning of a word like crepuscular? If in doubt, check.
5. Clarity is everything
Academic writing can be obscure and jargon-filled, but that doesn't mean it's good academic writing. Think of it this way: you've got ideas which you want to communicate to the reader, so you want them to understand your ideas as easily as possible. That means your writing needs to be as clear as possible. The flipside is, confused writing = confused thinking.
6. Everybody re-writes
Students are sometimes amazed when I tell them that re-writing is what everybody does. I think they assume that writing should be like taking dictation from the heavens. Well, apart from Mozart, that's never been true. Everybody re-writes, and their writing is miles better for it.
7. Read through aloud
Another one every writer should do. If you read aloud all those glitches, long sentences, lack of commas and so on become obvious. And by reading aloud I do mean out loud, not mumbling.