As Martin Bonner suggested, you or she need to check the local embassy. The U.S. Department of State has a page with some FAQs on applying for a passport from outside the United States.
I've cobbled together some information from other pages of the U.S. Department of State website.
A birth certificate is considered a primary identification IF it's issued by a city, county, or state. If it was issued by the hospital where she was born, it's a secondary identification and she would need further evidence.
She should double-check on whether she was issued a social security number. Sometimes you can apply while you're still in the hospital, but that might not have been true when she was born.
If she doesn't have a social security number, she will have to write a signed affidavit that states that she doesn't have one. Here's the wording from this FAQ:
“I declare under penalty of perjury under the laws of the United States of America that the following is true and correct: I have never been issued a Social Security number by the Social Security Administration.”
She would also need a passport photo which has pretty stringent requirements. There's information on the same FAQ page, but further down (new requirement as of 1 November 2016--no glasses allowed).