Technichally, you must advance in all three catagories; beating the Elite Four and the Champions, being an expert on Pokemon, and obtaining all the Pokemon in exsistance, of which, with the next generation coming, it's what seems to be impossible, and being ultimately unbeatable.
That's exactly one of the reasons why GameFreak and Nintendo continue along with its winding vastness of characters we know and love, called Pokemon; because we've just "gotta catch 'em all", don't we? I'll never acheive this goal...it'll take years to find the ultimate Pokemon master. Come to think of it, we never will.
Though, you can TRY to be the best in your neck of the woods...but the best in the world? C'mon, Nintendo; make a tournament.
As Evanji said, caring for your Pokemon with love is also important. Love and trust leads to power, via becoming a master of these well known beings.