I agree with Adalfu....if the essays, by virtue of their particular stories, require reference to the same story, then that is fine. You are completely right minime2 that the essays are short and you should not waste any of your valuable word count with repetitive information. Adalfu says 10% as a guideline, I would err on the side of re-using even less. However, you can avoid repetitiveness by focusing on different aspects of the achievements. For example, in E1 you could focus on the aspects of the achievement that would make you a good HBS fit, for example by demonstrating leadership. Then in E3-4, you could highlight the more personal aspects, how the achievement shaped your personality and approach to life.
Of course, if this is just not possible due to the nature of the story and if you will be repeating too much, then I suggest you choose an alternate E4.
Good luck to you!!!
Candy Lee LaBalle
mbaSpain