If you use a password Pokemon, it usually has power levels at 1500-1900.This gradually increases in power as you get more Wonder Keys from beating the Battle Royale at different ranks, until they reach their original power level. You will know if it has reached its maximum because the blue icon: (!) next to the Pokemon's name will be darker of colour (if it is still light blue, it can grow more.)
This also works with "Pokemon From Afar", those that your friends bring with their Wii Remotes.
However, for any other Pokemon, you have to keep catching the same Pokemon just at a higher Power.