Like all Pokemon Mew has a 1/8192 chance of being shiny. 
You can try catching it with action reply but be warned you can't trade it.
If you really want to trade or you have a gameshark but not an action reply you can warp to Faraway Island and use the battle Mew cheat over and over but it'll probably days and there are no guaranties, meaning you could spend 5 hours a day for a week and your not any closer to catching it than you were to begin with.
