Without using Action Replay or starting the game over, there is no way to re-battle Palkia.
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When you catch dialga/palkia or defeat them, you can catch azelf and uxie in the lakes.Mespirit will flee so you gotta get a poketech radar to track it down.
You need the Pokemon with arena trap in battle or the wild Pokemon can flee
After you catch the main legendary (dialga, palkia, giratina) go to lake verity and mesprit will be in the cave in the middle of the lake. Talk to it and then it will flee and appear on your map app.
Yes You Can i have hule pokedeck full.. yes
palkia