Your expereince and education reflects that you have a good industry overview. For consulting, you genereally should have 2 main skills - Problem Solving (With sttructure approach) and basic maths. I would say curosity also helps.
That being said, if you are applying for a role such as a manager or above, they would also expect you to have skills in leading the team, managing clients or developing relationships with junior clients. The range of work would depend from firm to firm(boutique or big).
Hope this helps.