A good move set for palkia is earth power,aura sphere,spacial rend,and hydro pump.This move set helps it give a large coverage against multiple types.Earth power would be great to take care of electric types one type that it is weak to.Aura sphere would be great to take care of ice types.Spacial rend will take care of other dragon types with ease.Hydro pump would be useful to take down fire types.In super training focus mostly on special attack and speed only.This will help your palkia out speed most other Pokemon and will make these moves stronger after super training it.All of these moves are under the beauty category so it will be great in beauty Pokemon contests if you wanted to know.Once you train it all the way to level one hundred it will be a very difficult Pokemon to take down.Try to get the stats close or between these numbers this is based off of my palkia.
Attack 240-255 Defense 230-250 Sp.Atk 385-400 Sp.Def 265-280 Speed 320-335
My palkia's stats are actually 248 for its attack 236 for defense 399 for special attack 277 for special defence and 328 for speed.If you wanted to know it's nature its timid which increases speed, but lowers its attack stat.
Good luck on making the perfect palkia.