Instructions
Go to Lilycove City, located to the east of the Safari Zone and northeast of Mt. Pyre.
Prepare your team. Go to the Pokemon Center and put Pokemon in your party that are level 40 or higher. Add at least one Pokemon that knows False Swipe and one that knows a sleeping move, like Sing. Head to the shop and buy at least 30 Ultra Balls.
Go to the docks at Lilycove City and stand by the ferry entrance. Save your game, and then turn off the Game Boy Advance.
Insert the Action Replay device into the Game Boy Advance. Insert "Pokemon Emerald" into the slot on the top of the device. Turn the power on. The game is recognized and you are taken to the code screen for it.
Add a new code named "Faraway Island." Input the code "8DEB234A 4C8DC5EC." Save the code and set it to "Active." Press "Start" to load your game.
Go through the ferry dock entrance when the game loads. You are automatically taken to Faraway Island. Save the game. Turn off the console and remove the Action Replay. Reinsert the game cartridge into the Game Boy Advance and start the game.
Head into the bushes to see Mew floating around. When Mew sees you, it hides in the grass. Look for its pink tail sticking out of the grass. Chase Mew around until you run into something that you can't see. You have bumped into Mew. Press "A" to battle Mew.
Use moves like Sing and False Swipe to make Mew easier to catch. If Mew falls asleep or its health gets low, start throwing Ultra Balls to catch it.
Go back to the previous area once you have captured Mew. Go south and then west through the bushes. Take the path to the ferry. Talk to the captain to go back to Lilycove City.