How Do I Meet Giovanni's Son in Pokemon LeafGreen?

Progress through the game until you are allowed to choose a Pokemon in Professor Oak's Lab. Immediately after selecting your Pokemon, your rival will challenge you to a battle. At this point, he will have only one Pokemon. If you chose Charmander, he will have Squirtle. If you chose Squirtle, he will have Bulbasaur. If you chose Bulbasaur, he will have Charmander. Whatever Pokemon you choose, your rival will pick the Pokemon that is strong against yours. His Pokemon will be at level 5.

Make your way to Route 22, where your rival will challenge you to another battle. Defeat him to advance. At this point, he will use his starter Pokemon and a Pidgey, both at level 9.

Defeat the first two gym leaders and travel to Route 24 for yet another encounter. This time, your rival will have his starter at level 18, a Pidgeotto at level 17, a Rattata at level 15 and an Abra at level 16.

Defeat the next two gym leaders and head toward the S.S. Anne in Vermillion City. Your rival will challenge you again. He will have all of the same Pokemon as in the previous battle, but the starter, Abra and Rattata will be in their evolved forms and at slightly higher levels.

Enter the Pokemon Tower for the fifth rival encounter after you have received another badge. At this point, your rival's team will change depending on what Pokemon he chose at the beginning of the game. If he chose Charmander, he will have a level 25 Charmeleon, a level 20 Kadabra, a level 22 Gyarados, a level 23 Exeggcute and a level 25 Pidgeotto. If he chose Squirtle, he will have a level 25 Wartortle, a level 20 Kadabra, a level 23 Growlithe, a level 22 Exeggcute and a level 25 Pidgeotto. Finally, if he chose Bulbasaur, he will have a level 25 Ivysaur, a level 20 Kadabra, a level 23 Gyarados, a lvel 22 Growlithe and a level 25 Pidgeotto.

Enter the Silph Co. Building in Saffron City for the sixth encounter after you receive the sixth badge. He will use the same team as before, but all of his Pokemon except for Growlithe or Exeggcute will be fully evolved and all between levels 35 and 40.

Travel back to Route 22 after receiving all eight badges to encounter your rival for the seventh time. He will use the same team as before, but at higher levels and with one extra Pokemon, a level 45 Rhyhorn. Defeat him to advance to Victory Road.

Defeat the Elite Four to challenge the final trainer in the game, the Pokemon Champion. The Pokemon Champion turns out to be your rival, and his team is much more difficult this time around. He will use the same team as before, but all of his Pokemon will be completely evolved and all between levels 53 and 61. Once you have defeated him, you can go back and challenge him again as many times as you want.