Refers to a certain type of female cyclist in New York City. Hallmarks are long flowing hair, no helmet, wearing stylish footwear, a dress, jewelry. Bicycles range from expensive designer "city bikes" to dutch city bikes to vintage American and English 3 speeds, most equipped with baskets or luggage racks.
Etymology comes from BikeSnobNYC, the Godzilla part is presumably due to the fact that these women are wrecking New York City.
I was riding on 8th Ave, but had to jump out of the bike lane when a herd of beautiful godzillas were salmoning towards me with their shopping bags swinging all over the place.