The episode is called "HOW'S BAYOU". It first aired on September 16, 1989, and it was written by Jeffrey Scott. In the episode, Kevin is lured into Bayouland, one of the many worlds in Videoland, to find his dog, Duke, who was lured there while chasing a robotic cat. Kevin was really bad at playing Bayou Billy back on his Earth. (The game looks nothing like our "The Adventures of Bayou Billy", BTW.) So, Kevin doesn't have the moves to survive in the swamp world. He meets Bayou Billy and his pet alligator, Loafer. Billy teaches Kevin how to use a whip and other weapons, rather than having to rely on his Power Pad and Zapper. So, Kevin is able to rescue his friends, Princess Lana and Simon Belmont, when they are captured while searching for Kevin. The episode ends with them having dinner together in the Bayou. Duke accidentally finds Loafer's nest, and he runs away from a whole bunch of baby alligators! This is odd, seeing as Loafer was referred to as a "he" throughout the episode. Oh, well...
The episode is really good, even though it doesn't rely on the game that much. Also, Billy has blue facial hair. Odd. The episode has two different versions. Version 1 aired only on September 16, 1989. I have a copy of version 1 from a friend. I have version 2 taped from reruns on the Family Channel. The list of known differences between the two versions can be found here.
The episode has some great music. Here is a partial listing. All of these are in version 2. I'll list the version 1 music later.
Underground and Fortress music from Super Mario Bros. 2
'Born On The Bayou' by Creedence Clearwater Revival (not performed by them)
'Brinstar' music from Metroid
I have yet to check if any of the music from the game is in the episode.
If you want to read a novelization of version 1 of "HOW'S BAYOU", go here.
If you want to read a novelization of version 2 of "HOW'S BAYOU", go here.
If you want to read a novelization of the canonical version of "HOW'S BAYOU" that I prepared, go here.
Bayou Billy also made a quick cameo appearance in the episode "HAVING A BALL" in 1990. It was written by Dennis O' Flaherty. Princess Lana is throwing a royal ball at the Palace of Power.
Finally, when Zelda collapses on the floor, Billy is among the many people that gather around her.
I'll try to get more screen captures from these two episodes soon!