Note that since King Hippo is a regular character in Captain N, only his debut is described in detail, not his role in every episode, unless it features additional references to the Punch-Out!! series.
Captain N: The Game Master episode Kevin in Videoland
September 09, 1989
King Hippo from the NES game Punch-Out!! is a recurring villain in the series, being one of the two main servants of Mother Brain, the show's main villain (the other being Eggplant Wizard). He's introduced in the first episode and his appearance is slightly altered from his original look, most notably sporting a light blue skin for unknown reasons. His main characteristic is his incredible strenght. In the episode "Metroid Sweet Metroid" he's also brefly seen leading a group of boxers, however these are not characters from Punch-Out!! He appears in every other episode in the series except the ones where Mother Brain doesn't appear.
Also, in the fist episode (a scene reused in every episode's opening), Kevin is seen playing Punch-Out!! before being sucked into the TV and to Videoland. Specifically, he's seen fighting King Hippo. A minor animation error is that the first time the game is shown on the TV, the gameplay footage is zoomed in, and the stat bars on top of the screen are missing.
A minor reference to Punch-Out!! is Mother Brain telling King Hippo "go to the palace and punch out their defenses!"
Captain N: The Game Master episode Videolympics
September 30, 1989
The fourth episode of the series is about Mother Brain challenging the N Team to the titular olympic-style competition. The villains are then seen training in the "Punch Out" world, whithin a big gym. This is the only appearance of this world.
In the gym can be seen a very weak blonde boxer, who is likely based on Glass Joe. He is briefly seen training against his own shadow and losing (notably this scene has an animation error, since it takes place in the background, but overlaps a punching bag in the foreground). There also is a red-haired character, but he doesn't resemble any specific Punch-Out!! character.
Additionally in the gym there's a poster for a boxer called "Big Moe", possibly a pun on "Little Mac".
Captain N: The Game Master comic
The first episode of the comic, titled "Welcome to Videoland", starts with scenes from various videogames, and one of these is from Punch-Out!! showing Little Mac punching King Hippo (depicted with blue skin like in the cartoon). King Hippo is also shown as a member of the league of darkness, but unlike the cartoon he's not a regular character, only making few appearances. The times he appears, however, his role is the same as in the animated series, being Mother Brain's servant along with Eggplant Wizard.
Copyrights for both series are held by Nintendo.