You may be technically correct, but (with the usual caveats about trusting Google) "win the Nobel" gets over 4 million hits and "win a Nobel" almost 1.75 million. (9.5 million for 'awarded a/the Nobel, to be fair.) I don't think using "win" would raise many people's eyebrows, certainly not mine anyway!Marie Curie was the first woman to ........ two Nobel prizes.
I don't think one either wins or achieves Nobel prizes.
They are awarded by the Nobel Foundation.
Marie Curie was the first woman to be awarded two Nobel prizes.