You cannot get Shadow Lugia on any game except Pokemon XD: Gale of Darkness without hacks (AR is not a truehacking device).
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There is no Action Replay code in order to get a Shadow Lugia in Pokémon Pearl.
no, sorry.
i don't believe so. the only way you can get a shadow lugia is on xd gale of darkness. and even then, you cant trade shadow Pokemon to gb/ds games. you have to purify them first.
Action Replay
There is no such thing as the Shadow Luiga. To catch the Shiny Lugia though, you need to find the code.