Pre-series
As revealed in a flashback of the special's Japanese theme sequence A New Oath, Vincent obtained Meganium as a Chikorita from Professor Elm on the same day that Jimmy got his Cyndaquil and Marina got her Totodile. It had already fully evolved by the time The Legend of Thunder! aired.
When Vincent suddenly arrived on the scene to stop Team Rocket, Meganium saved Jimmy and Marina by using a Solar Beam on a big rock coming from Steelix's Rock Throw that was heading for them. Meganium attacked Steelix with Solar Beam but it was proven ineffective.
Later, Meganium participated in the effort to save Raikou from Attila and Hun as Vincent had it use Solar Beam on the crystal-generated field along with Little Miss's Psybeam, as any non-Electric-type move could neither absorb or reflect it. Later, it worked together with Typhlosion to take on Attila's and Hun's Pokémon. Around the end of the battle, Steelix was about to finish them off with Crunch, but it was stopped by Raikou, who had managed to escape from Team Rocket's Crystal System.
Meganium is seen once more as they all band together to celebrate their victory against Team Rocket.
Meganium and Bulbasaur's rivalry
In Tie One On!, during the Silver Conference, Jackson* first wanted to save Meganium for the Victory Tournament, but realized that it was a mistake for him to do that. Outside, Meganium, along with Azumarill, got into a rivalry with Ash's Bulbasaur and Squirtle respectively as they wanted to have the one apple that was hanging on the tree. Harrison's Miltank arrived and stopped them however with Heal Bell.
During the battle Jackson had with Ash, he sent out Meganium when two of his Pokémon were already defeated. Meganium was tied up against Bulbasaur. Both of the Grass-type were still upset about each other for what happened before. They recklessly used their attacks on each other, not bothering to evade any of them. As they both used Solar Beam, both of them were knocked out, ending the battle in a draw. Despite that, the Grass-type Pokémon started to get along, shaking vines.
It reappeared in a flashback in Pace - The Final Frontier!, when Ash remembered Bulbasaur's battle with it.
In Pride of a Champion!, Meganium reappeared watching the Masters Eight Tournament match between Lance and Diantha on TV.
Meganium is Vincent's most powerful Pokémon. Despite suffering a lot of damage in the battle against Team Rocket, it, along with Jimmy and Marina's Pokémon, managed to destroy the barrier that held the Legendary Pokémon. During the more peaceful Silver Conference, Meganium shows more of its personality, being quite provocative when bullying Ash's Pokémon. Meganium also developed a rivalry with Ash's Bulbasaur, during which it became more proud and decided to take a more serious tone.