From the Super Mario Wiki
Goomboss, also known as the Goomba King, is one of the first bosses that Mario and Goombario encounter in Paper Mario. He later reprises his role as a boss in the games Super Mario 64 DS and Mario Kart DS. It is noted that he is one of the only Paper Mario series characters that returned in other Mario games, along with Koopatrols and the Star Spirits. His name is a portmanteau of "Goomba" and "boss".
Paper Mario series
In Paper Mario, he was originally an ordinary little Goomba, but Bowser used the Star Rod to make him a king (which also greatly increased his size) under the conditions that he would assist Bowser later on. He is first seen when the Goomba Bros. come to his fort wailing about their defeat to Mario. He lets them in his fort, and when Mario comes by, he has a short conversation with him and then engages him in battle along with his minions.
In battle, he is accompanied by Red Goomba and Blue Goomba. Mario will find him by his Fortress. The easiest way of defeating him is to hit the Goomnut Tree at the start of the battle to make one giant Goomnut fall on him and the Red and Blue Goomba, doing three damage and instantly knocking the weakened Goombas out. When the Goomba King is defeated, he surrenders and retreats to his fort while pleading that Mario will not press a nearby switch. When Mario presses the switch, the fort reveals to be a bridge used to get to Toad Town, and he and his minions fall into the abyss, defeated.
While Mario battles the Goomba King and his lieutenants, Red Goomba and Blue Goomba, Kammy Koopa is secretly observing the battle. She reports back to Bowser, who is furious at the Goomba King's defeat and also yells "I only used the Star Rod to make him a king because he begged me to...".
In the ending parade of Paper Mario, Red and Blue Goomba are trying to get the Goomba King out of a tree. He then falls out, and dizzily wobbles off the screen, followed by the Goomba Bros.
Paper Mario: The Thousand-Year Door
Super Mario 64 DS
He also appeared as a boss in Super Mario 64 DS, now called Goomboss. The battle arena can be reached after eight Power Stars are collected. The way to defeat him as Yoshi is by eating Goombas and spitting them back at him in the form of an egg to win back Mario's key to unlock him as a playable character in the game. However, Goomboss starts getting faster and angrier after every hit and also gains more Goomba followers. He needs to be hit three times in order to admit defeat. When returning back to fight him once again as Mario, Luigi, or Wario, they can punch him in his face and obtain a Super Mushroom. Using it and attacking him while under its influence is not required to defeat him; the player can just punch the Goombas into him to damage him. After he is defeated, Yoshi gets the Mario key, which is used to unlock Mario. This appearance also proves that he knows Luigi but he does not know Wario.
Mario Kart DS
In the missions section of Mario Kart DS, Toad must complete three laps of the Baby Park course before the Goomboss does. After each lap, Goomboss becomes bigger and angrier, but he has to stop for a few seconds to grow, giving Toad a chance to pass him. Another chance to pass him is when he stops to throw one Goomba on the first lap; one or three Goombas on the second lap; or one, three, or five Goombas on the third lap. If Toad hits a Goomba, he will lose one of his three balloons. If Toad loses all three balloons, he will fail the mission. But Toad will not lose a balloon if he hits Goomboss. Occasionally, Goomboss will throw a Mushroom instead of a Goomba, allowing Toad to get a boost of speed. Additionally, on the third lap, Goomboss will cheat and Hop over the center divider, improving his chances of winning. If Toad is in front of Goomboss, he will not stop to toss Goombas but will run as fast as he can to catch up.
Names in other languages