I suspect you have a specific client situation in mind; my answer is somewhat generic, since you have not been specific.
I am not sure how you define a ‘difficult’ client. Do you mean somebody who is not compliant with your exercise recommendations? I find that you need to meet with client where they are and talk at the same frequency. To use exercise compliance as an example: there are recommendation about how much and at what intensity a person should exercise per week, and, as trainers, we try to nudge people toward that goal. But if they are not ready to such a commitment, then your gentle nudging will be perceived as unwanted nagging, and you will not succeed and even turn off the client altogether.
An introvert personality may have a harder start as a personal trainer in getting clients. A person of that inclination rarely toots his or her own horn even if the qualifications and knowledge are there. But if you can demonstrate through results that you are a good trainer, then people will notice. Particularly when you train at a gym, you are always observed by many more people than your think.
Hope this helps.