The Old Sea Map was only available as an event Key Item exclusively for players with a Japanese copy of Pokémon Emerald,
which allowed players to reach the Faraway Island, and ultimately battle the Mythical Mew.
For players who rather not use the Mystery Gift to activate the event, simply use PKHeX's Event Flags > Research, and
For Pokémon Emerald: Check Flag 0316 and 2262, then proceed to add a Old Sea Map into the Key Items of the Bag.
This is the only Mew that can be encountered shiny legitimately. (excluding hacks or glitches)
ウルトラ Mew was a regular encounter, non-shiny.
ポケパ-ク Mew was RNG obtained by @suloku and @St. GIGA (and the OT was meant to mimic the PokePark event, and also Flawless IVs)
アイコ Mew was RNG obtained by @InsaneNutter
Format Ver.1.0.6-2, Post Updated Date:20180512_0857