To capture Shadow Lugia go to Citadark Isle and you will get an E-mail from Prof. Krane go to the Pokemon HQ lab go to where the simulation where you started the game at in front of the entrance to it there will be an old man there. Talk to him then go to where you got the Snag Machine and then do everything that Prof. Krane and he will give you a Master Ball beat everyone at Citadark Isle then you will face Master Greevil he will start out with Shawdow Lugia use the Master but leave an empty space in your party! He has powerful pokemon and are all Shadow pokemon! And three of the six are Legendary! But don't worry you can face him as many times to Snag all of his Shadow pokemon. His regular pokemon are very strong after you beat him and snag some of his pokemon. Hope I have helped!