First of all, it's not often that you get fired in management consulting. There are many reasons for this (for example, the rigorous recruitment process, the supportive culture focused on development). However, in difficult economic times, certain companies will significantly restrict hiring and raise the level of promotions. Briefly explain the reasons why you're firing the consultant.
You don't need to provide specific details or incidents. If you fire her for poor performance, tell her that you can't justify the costs because of a lack of results, but don't be rude or accusatory. You may think that the time has come to fire the consultant, but you fear ruining your relationship with someone who keeps a lot of company secrets or who could easily help a competitor. There have been people fired from Barclays for manipulating the book and all kinds of unethical nonsense that is hired by the buying side or by another big company.
Now, at the beginning of this email, I mentioned that offending customers was just one of the three main mistakes that new consultants make and that cause them to be fired. Fortunately, it's actually much easier to get good results in consulting (in my opinion) than it is to get a job offer in consulting.