Investment banks always look for best of the best. What if you have a relatively weak resume, with your GPA below 4 and not graduating from famous institutes like Harvard or INSEAD? Though 'to hire the best' is the rule, but sometimes people don't work to rule. Some very senior bankers do have only a basic degree without much outstanding academic credentials. And in my other posts, you would find some very senior executives even had no qualification at all.
To start your investment banking career, personality fit is more a determining factor rather than skill sets or academic results. However to persuade the hiring manager to grant you an interview and to find out more on your personality is a separate issue.
My peer, Jimmy Sweeny, always reiterate that an amazing cover letter will generate interviews, even with a relatively weak resume. You might want to browse his website and get some insights from him. Of course you can browse through my blog for more tips about writing an effective cover letter.
Investment Banking Cover Letter