First, recognize that it isn’t helpful or healthful to take the behavior of difficult people personally.
Second and perhaps more importantly, what you need to realize is that you aren’t going to change or fix them. It isn’t your job and I don’t think you really want that job anyway. No one - and I repeat no one - changes their behavior unless and until they want to change their behavior. So, what can you do? The only person you can change is yourself. So, focus on changing your pattern of emotional and behavioral response to the difficult people in your life so that you make healthy and productive emotional and behavioral choices that benefit you now and in the long term!
Third, manage your emotions in your dealings with these people. Learn to depersonalize their behavior. This is what I suggested at the outset and is perhaps the most important piece of advice I can offer. Don’t become defensive with your difficult person. This will only fan the fire. Don’t play their game (it may be a game in their mind by the way even if it is not a game to you). Recognize that they act the way they do because this strategy believe it or not has worked well for them before in similar situations. This doesn’t mean that their behavior is positive, healthy, or that it produces the results that you or I would consider productive but rather that it meets their needs, emotional or behavioral, not necessarily in a rational or productive way that you or I would understand. Don’t expect or try to understand them as this isn’t going to change these people or their pattern of behavior.
Do seek support from others. Depending on the seriousness of the situation, you may find it useful, for example, to keep a dated written record of your interactions with your difficult person. Depending on who the difficult person is it may be useful to discuss the situation with your advisor, a trusted friend and/or colleague. Consider seeking professional support through your Human Resource Management department.
Finally, as with anything in life, recognize that dealing with difficult people is a skill worth learning and that as a skill it is one you can cultivate with practice. Commit to assess past incidents and learn from them: Who was involved? What happened? How did you feel? How did you respond? How do you wish you had responded? What could you do differently in the future to affect a positive outcome to a similar incident?