My healthy client often feels nauseous and dizzy after high intensity intervals. Is there any way to help this?

Sounds like the intervals are too much. I would back off. Make sure he or she has a good fitness level first. Work on endurance and lower intensity exercise to get a good base. If he or she already has good strength and endurance I would check with the physician. Make sure you have the all clear.
Once all that is done I would start back with just 10 seconds of higher intensity (not as high as what you are doing now), give a good two minute rest period of very light intensity, and if that is tolerated do just one or two more intervals for that session. Make sure there are at least 1-2 rest days, and try again, very gradually lengthening the interval time and number of intervals, then reducing the rest intervals. High intensity has a lot of benefits, but also risks. Rest is very important during the session and in between sessions.