Odds of Getting In
The world of credit analysis isn't exactly one that requires breaking into. It's much more of a "make an appointment, wait in line, then be quietly ushered inside by a distinguished-looking butler" sort of thing. As with most math- and science-oriented careers, you either have the skills or you don't; there's not a whole lot of room for qualitative error.
Earning the credit analyst business card is about taking the right steps. Go to college, study finances, get your degree, get an entry-level job, and work your way up. It's as easy (or as difficult) as that.