You automatically get a key item called the Miror Radar in this game. It will automatically notify you if Miror B. has been seen. He will always have a Shadow Pokémon that you failed to catch, unless there are none. Sometimes he'll have Shadow Pokémon of his own.
To purify XD001 Shadow Lugia, you must have nine Best Circles in the Purify Chamber. A Best Circle is when you have four normal Pokémon there, facing one another so that one has a type advantage against the one it's facing, continuing in a circle. One example is Vulpix at the top, who faces the Shroomish on the right, who faces the Blastoise on the bottom, who faces the Sandslash on the left, who faces Vulpix. And before you ask, no, you can't get Squirtle in this game. I just used Blastoise for that example because he was the first Water-type I thought of.
