I've seen a lot of people ask this recently. Well, I've tried to explain it as best I could, and concluded that it's the best explanation I've ever read. Call me cocky.

Well, here's my explanation, updated and upgraded.
=====================================
To purify XD 001, AKA Shadow Lugia, you have to get all 9 purification chambers up to maximum tempo.

This can be done by placing a pokemon that has strengths against the next pokemeon. Since nobody EVER knows what I mean by this, I'll give you an example.

Water
Rock
Flying
Grass

How does this work?

Well, water is super effective against rock, rock is super effect against flying, flying is super effective against grass, grass is super effective against water. So you could place, for example, a Remoraid in the first slot, a Geodude in the second slot, a Pidgey in the third slot, and an Oddish in the final slot. I'll give some more examples to get you half way there.

Fire
Grass
Water
Ground

Example: Vulpix, Oddish, Magikarp (I'm serious, it works), Sandshrew

Psychic
Fighting
Dark
Ghost

Example: Abra, Machop, Umbreon, Gastly

Normal
Normal
Normal
Normal (this one DOES work)

Example: Skitty, Skitty, Skitty, Slakoth!

Once you've maxed out the tempo of all chambers, simply place Lugia into one of them and he'll immediately be purified. Congratulations, you can now use Lugia, trade him to your GBA game.

This will be his moveset once he's purified:
Psycho Boost
Feather Dance
Earthquake
Hydro Pump

If you still have some pokemon to purify, remember that the tempo is maximum in EVERY chamber. This means you can purify your shadow pokemon in no time!

I hope you take heed of this guide. If you have any further questions, please contact me. Good luck.

This message was edited by Relmutsie AN on May 11 2008.

one little Q Do all the boxes HAVE to be different or can they be the same?

They can have any order you want.

You can also put all normal types together to create a perfect tempo.
Ex.
Normal
Normal
Normal
Normal

the center pkmn must attack(the pkmn connected to him)and be super affective
ex flying/fire(moltre)vs bug/figth (heracross)

fire==>bug=super affective
flying==>figth=super affective

super affective+super affective=perfet combo!

you must as much as possible to make many combo like that
(i know becaus i have purified lugia)

Sorry, but I believe what you guys just said was already mentioned in the first post...?

I have not purified the lugia and this stinks!
I am selling my game!