OK then. You want Palkia. To get Palkia, you must have:
Played through the storyline and beaten Dialga at Temporal Tower
Played right to the end and beaten Darkrai
After doing those two, you will have already fought Palkia. You must return to a dungeon called Spacial Rift, get through all the floors and battle Palkia again. After you win against Palkia for the second time, Palkia will ALWAYS join you. Good luck.
3DS FC: Snail 4527-8592-7979