Becoming an investment banker is pretty difficult. Unlike many highly-paid professionals, such as anesthesiologists or actuaries, you can't just go to school, learn what you need to know, and get a job. You have to go to the right school and learn what you need to know.
While that may sound a bit more like your odds of getting a job rather than the qualifications needed to get a job, in this rare instance, they're one in the same. If you don't go to a top-tier business school, big banks won't consider you good enough to hire. Sure sounds like a qualification to us.
Assuming you get into Harvard or Wharton, you'll need to nab a degree in business with a focus in anything money. Afterward, you can jump up the ropes in a firm as an analyst or try for your MBA right off the bat. Once you're in, though, you're in.