There are no downsides in applying for an internship at McKinsey before you graduate, so definitely go for it.
I would also recommend you don't apply to McKinsey only, but to all the main consulting companies to increase your odds of an offer (a Tier-2 internship will increase the chance to be called by McK when you graduate if you can't land an offer now).
There are three main things you need to be invited for interviews:
- A great CV
- A great Cover
- A referral – the more senior the person the better
For the CV, you can work on the following in the time you have left:
- Internships/work experience in relevant companies (other consulting firms, IB, strategy roles in big brands, entrepreneurial initiatives)
- Volunteer/leadership experience
- University achievements (if applicable): top GPA, exchange, university clubs
If you are planning to apply to B-School, you may also prepare the GMAT (not worth just for the sake of the application)
For the Cover, you can structure it in 4 parts:
- Introduction, mentioning the position you are interested in and a specific element you find attractive for that company
- Why you are qualified for the job, where you can report 3 skills/stories from your CV, ideally related to leadership, impact, drive and teamwork
- Why you are interested in that particular firm, with additional 1-2 specific reasons
- Final remarks, mentioning again your interest and contacts
In part 2 – the one you are referring to – you can write about experiences that show skills useful in consulting such as drive, problem-solving, leadership, teamwork and convincing others.
It is important that in part 3 you make your cover specific to a particular firm – the rule of thumb is, can you send the exact same cover to another consulting company if you change the name? If that’s the case, your cover is too generic.
For referrals, you can find a step-by-step approach at the following link: