> How much math do I need to approach NLP in a way that enables me to be among the best?

The best in what? If you mean pushing the boundaries of research, yes, then your path there will likely involve a PhD. If you mean building the best technology products, then being able to read, understand and implement the biggest recent advances is enough and usually requires far less mathematical knowledge.

(That was intentionally written generically since I think that it applies to more than just NLP)