Hey, I was wondering if someone could tell me how to purify shadow lugia...

Here's a tip: If you put 4 Normal type Pokemon in a ring, the tempo gets maxed out. Try Snorlax, Kangaskhan, Chansey and Lickitung or something along the lines of that.

~ Spyro ~

You do need all nine sets done, but for each set, you need an advantage for each Pokemon to have a full tempo. For example, 4 Pokemon like Numel, Mareep, Spheal, and Seedot. 1.Numel works against Mareep. 2.Mareep works against Spheal. 3.Spheal works on Seedot.
4. Seedot works against Numel.
(then back to number 1)

Have all those advantages on all nine sets, put Lugia in any set, then POOOF! So quickly, Lugia is purified.

Note: Even though I can't tell you all 36 Pokemon for all nine sets, but I can tell you this: Find 4 different kinds of Pokemon that can have an advantage on each other (like an "Advantage Circle.")

Get 36 purified shadow Pokemon.

When you put your Lugia inside the purify chambers, and they're maxed out, when you try to exit, it might say something like, Somethings different about the lugia. Here's your chance. Rush back to headquarters, and go to the room in which the giant purifier machine is. The lady by the center of the room will tell you there is a Pokemon ready to open it's heart. Step in the center, and press "a". Press it again when you see the holographic images of your Pokemon, wait a few seconds, and then, voila! You have a pure Lugia. hope that helped, and, as always,
Happy training.