What single-player mode in the original Mario Party has players clear every minigame?

The single-player mode in the original Mario Party that has players clear every minigame is Mini-Game Island.

Mario Party, released for the Nintendo 64 in 1998 in Japan and in 1999 in North America and Europe, includes the usual multiplayer Party Mode plus several specialized modes. Mini-Game Island is the original game's campaign-style challenge: one human player travels across an island map, playing minigames in sequence.

The player begins with four lives. Winning advances the player and awards coins, while losing costs a life. Collecting 100 coins grants an extra life, giving skilled players a way to recover during the journey. The goal is to complete the game's full set of 50 minigames, rather than compete for Stars on a traditional board.

A common mix-up is Mini-Game Coaster, which is the comparable single-player progression mode in Mario Party 2. Mini-Game Island belongs to the first game; completing it also unlocks bonus Bumper Ball Maze content in the Mini-Game House.