This event was distributed to players at the New York Pokemon Center: Gotta catch 'em all! Station,
and the machine were distribuing various PCNY Pokémon across the period of November 22, 2001 to March 13, 2003.
The schedule of Pokemon changes weekly, and players were restricted to collecting one Pokemon per week per visit,
and the restriction was enforced by the distribution machine; it checks for data stored in the Gen 2 save itself.
It appears that the data stored is the header/title, which is checked against the distribution data.
This Mew has a 0.5% chance of occurring, and was always distributed as shiny.
A more comprehensive schedule list can be seen here.
The event that had Mew ran from November 22, 2002 to November 28, 2002.
DUE TO HAVING AN EVENT LOCATION,
THIS POKEMON WILL NOT BE LEGAL ON ANY VIRTUAL CONSOLE RELEASE.
If you want more Shiny Mews, or various other PCNY mons, @Deoxyz has compiled a save containing mons received from the PCNY distribution machine here.
If you want to learn move information, check out these videos. [Q&A vid]