Is "in in vitro" acceptable?
English has compound words that have an space where one might otherwise see a hyphen. Since in vitro is a loanword which behaves as a single lexeme, use it as such.
For purposes of euphony and clarity, I'd probably word it "advances within [the field of] in vitro fertilization".
It offends no principles of grammar or good usage that I am aware of, but if it discomfits you, try saying instead "in fertilization in vitro".