Catching Mew in 'Pokémon X' feels like chasing a legend—because technically, it wasn't meant to be available in that game! The original Gen 6 games didn't include Mew as a catchable Pokémon, but there are still ways to get one. Trading is your best bet; some players offer Mews through the GTS or Wonder Trade, often from older events or other games like 'Pokémon GO'.
If you're into glitches (and don't mind bending the rules), there's a convoluted method involving the Pokémon Bank and transferring a Mew from earlier generations. But honestly? I'd wait for a special distribution event. Nintendo occasionally releases mythical Pokémon like Mew for free—just keep an eye on announcements. Until then, maybe shiny hunt something else to pass the time!