A Youtube Vid door AltEisenSpirit on how to get Mew without cheats. I haven't tried it yet so I don't know if it works. I'll try as soon as I soon as I can. I started a new name on my brand Red yesterday so I'll get to is ASAP.
This is how to catch Entei, Suicune, and Raikou in brand Red. It's made door pokeparty01. I don't know if it works yet though, I only have the first badge in brand red right now. Enjoy and hope it works!