In answering this, do not list accomplishments from high school; they do not matter. If you recently graduated college then it is okay to talk about the feats you have accomplished in college. However, if you have been in the work force for several years, then you need to talk about accomplishments that are career-related, and hopefully closely related to the job you are applying for. It is okay to spice up your accomplishments a little but make sure not stretch the truth too much. Some examples of accomplishments worth noting are:
Refrain from answers such as “I work too hard” or “I have trouble leaving tasks unfinished.” These answers are too clichéd and you can bet that many of the people in the interviewing pool will answer the question with those answers. Your answer should be truthful yet memorable. Be honest about your weaknesses but also talk about what steps you have taken to improve upon those weaknesses. For instance, you can say that you are not a particularly adept public speaker. However, as an addendum to that answer, you can also say that you are taking steps towards be more comfortable on stage by going to Toastmasters meetings, volunteering for more speaking engagements, or even taking a public speaking class. Employers love employees who take the initiate to improve upon themselves.
As an additional tip, it is best to choose a weakness that doesn’t particularly affect the job you are doing. In the example of public speaking above, you can use it for jobs that do not involve speaking in public. However, if the primary purpose of the job you are applying for is to speak in public, then you have pretty much all but disqualified yourself from the job if you answer the interview question with that answer.