There is no way. You only can get a shiny luigia that its color is red.
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no, sorry.
You cannot get Shadow Lugia on any game except Pokemon XD: Gale of Darkness without hacks (AR is not a truehacking device).
There is no Action Replay code in order to get a Shadow Lugia in Pokémon Pearl.
There is no such thing as the Shadow Luiga. To catch the Shiny Lugia though, you need to find the code.
Shadow Lugia is only available in Pokémon XD: Gale of Darkness and is fought as part of the storyline. You're able to get a Master Ball prior to fighting Shadow Lugia, so catching it shouldn't be a problem and needs no cheat code.