Employers ask difficult interview questions for a reason – they demonstrate your thought process, self-awareness and problem-solving skills. Anticipate the questions and practice your replies, modifying them on-the-fly to fit the specific situation:

• Tell me about yourself? Why are you leaving your job? What are your strengths? You have already developed your elevator pitch, modify it fluently and confidently respond to these types of questions.
• What management skills do you need to improve? What critical feedback have you received? Your response to these types of questions will demonstrate self-awareness and problem-solving skills. Be honest! 
• How do you handle stressful situations? Give an example and explain your approach and the outcome.

These and other difficult questions can sway the job search in your direction if you are calm, ready and practiced.