HOW CAN I GET ALL THE LEGENDARY'S IN THE WORLD OF POKEMON ON A SINGLE GAME WITHOUT A ACTION REPLAY OR WEB SITE??

by going to events for example the ones at game stop. or just trading with people, and transferring some of them from the older games.
that's the only way to get them with out cheating.

Trading, transferring, and distributions at GameStop.

You need to trade them all over if you have them from previous games or other people, or get them from an event.