I was recently speaking with a partner from one of this country's largest firms. He said that they hire approximately 2% of all entry level applications to their law firm.
That's out of a candidate pool of hundreds. He joked you had to almost have a Nobel peace prize to be considered. Maybe it wasn't a joke after all.
If working at a big law firm is what you really, truly want to do then here is a short video of an ex Attorney General asking a managing partner of a big firm what they're looking for in an entry level lawyer.