When you need to write an essay to a very short deadline, it's tempting to respond to the time pressure by starting to write immediately before you have taken time to plan out the essay. Although this seems to be a good way to beat the clock, it actually may result in your missing your deadline.
Before you start writing the essay itself, write an outline. Your outline should include your main thesis (which will be your introduction), three examples or supporting points (which will be your body paragraphs), and a conclusion showing how the body paragraphs support your initial thesis.
Set up the outline in your exam book as a set of 5 headings and fill in each section, allowing 5 minutes per section. If you get stuck on one section, move on to the next one. When you have something written for each section of the essay, go back and revise.