There is no way of getting Mew in Fire red/Leaf green. There was a hack in the older games that Gamefreak removed for Fire red and Leaf green with which you were able to obtain it.
The only way to get it are cheats, sorry.
The only way to obtain a Mew is by using a cheating device or promotional events.
Since the events for it are no longer available that's your only option.
Hope I helped.