In order to score (in multiplayer mode), players must lay time bombs in order to trap and obliterate their opponents, with the last player alive becoming the winner. As the player defeats enemies and clear away obstacles, a variety of power-up tiles appear. Randomly selected from a pool of 10 different items, these tiles have a number of effects, such as increasing bombs' blast radius, increasing the player's bomb capacity, or even reversing a player's controls.
Unlike other Bomberman games, Tournament's single-player quest mode is an action-adventure game with influences of Zelda and Pokémon.
The majority of the action takes place in 2D from top-down vantage point, while Karabon battles and select minigames are presented in a side view. Each of the game's six different environments possesses only a minimum of rectangular features and is detailed with all sorts of wacky nuances, such as trees that topple over or an earthen giant collapsed in the middle of a road.
On the edge of the galaxy sits a small planet, Phantarion. From the cutscene at the beginning of the game, it is given that five meteors (the five Dastardly Bombers, from Super Bomberman 2 and Super Bomberman 3) hit the planet. Shortly thereafter, a large fortress was erected, and in turn the land around the tall, tower-like fortress and the fortress itself began to freeze over. The people of Phantarion sent out a distress call, and Professor Ein sent Max to investigate. Upon arriving on the planet, Max makes his way to the base of the tower. Once inside, he is confronted by a huge bird creature (later found to be Plasma Bomber in his transformed state). He is knocked out by the bird by one fell blow, and is either sent to the top of the tower or down a hole (the exact cannot be determined, Max is only shown being pulled into a dark, foreboding circle in the center of the screen). When Doctor Ein talks to Bomberman a week later, Bomberman tells him that they have lost all contact with Max. Bomberman is then sent by Ein to save Phantarion and find Max, thus beginning the playable portion of the story.