The best way to combat this behavior is to employ the hard look. Look them directly in the eye with a straight, unemotional face. Stare right at them, and above all, do not look away. If you can't bear to look at their eyes, focus on their forehead. Hold the hard look long enough, and they will look away. They may try to get into your face or say something else critical, but don't back down. Stand your ground and continue to give them the hard look. After they have turned and walked off, you can then leave.
Learning to use the hard look isn't easy. It takes courage and practice. Start by looking everyone you talk to directly in the eye. This is not intimidation on your part. It signals confidence in yourself and respect for the other person. You may have spent your whole life thinking that you shouldn't look people in the eye. This is not a good technique for success in life.
Practice the hard look by looking at yourself in the mirror with a determined hard look. See how long you can hold it -- no flinches, no looking away. Then imagine that the person, who has been intimidating you, is the image in the mirror, and focus on your hard look. It may take some time, but you will develop the skill. And every time you use it in nasty encounters, you will become better at it.
If someone who outranks you, is saying critical things to you, employ the unemotional hard look and say nothing in return, other than "Yes, sir/sergeant."; "No, sir/sergeant"; or "No excuse, sir/sergeant". Do not let them suck you into an argument and do not look down. If they challenge you by demanding to know why you are staring at them, do not respond. If what they have told you is correct, as in something you need to change, then make the change. Don't waste time dwelling on their poorly presented correction. In the military, giving a senior leader the hard look is not a violation of the UCMJ. It might piss them off, but you can't be court martialed for it. In most cases, these leaders will leave you alone after one or two of these hard look encounters.
You are a person with talent and abilities. Stand up for yourself, when someone attempts to intimidate you with critical, nasty remarks. Keep your hard look ready for action.