To have that you have to catch 50-60 unique Pokemons.
That means, for example, if you catch two Onix, it will be counted as one unique pokemon. Here are the conditions to fulfill to get Exp Share: There is no other option except this by which you can get the exp share until and unless you play the Modified Version of Pokemon Fire Red or Leaf Green.
Conditions to get Exp Share in Pokemon Fire Red or Leaf Green.
