the criteria considered in consulting for hiring (either full time or internship) are normally the following:
- University reputation
- Academic performance
- Work experience
- Extracurricular activities
- Experience abroad
Given that you cannot change your school reputation and your GPA is not strong, as for a previous post I wrote you may work on the remaining points, that is:
- Degree: try to specialize in math/quant subjects
- Work experience: find internships in business/strategy related fields before applying for consulting, if possible with big brands
- Extracurricular activities: start activities in your universities, in particular in clubs related to consulting or activities that would involve interaction with C-levels (eg conferences organization with relevant guests and/or fundraising)
- Experience abroad: take part in an exchange programme
A good referral would also be very useful to receive an invitation.
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As for the consultancy, so far that you can satisfy the previous requirements you could have a shot for every type of firms. Of course, the less you satisfy them, the more you should go down the list in terms of prestige in order to get an interview. Since at the moment you do not have relevant working experience and strong GPA, it may be a good idea to try to get an internship at non-MBB firms, and then if still interesting for you move to applying for a full time position for top firms such as MBB once strengthen your CV.