Gossick World:

Get all 24 Other-Dimension Bombs and a 5 on every stage (Bomber Star
through Garaden Star).

Slider Race:

To get the first ??? on the options screen, get all 5s on all the stages
(Bomber Star through Garaden Star). In the Slider Race, you race a
snowman on your Bomber Slider with the best time recorded.

Golden Bomber:

To get the second ??? on the options screen, get 5s on all the stages
(Bomber Star through Garaden Star) and beat Gossick. In this mode a
gold card will turn Bomberman into Gold Bomberman. The best score from
three stages will be recorded. 

Millian's Treasure Hunt:

To get the third ??? on the options screen, get 5s on every stage (Bomber
Star through Gossick). In this mode, a ship returning from Garaden Star
filled with treasures blows up and scatters 24 treasures around all six
stars. Your goal is to find all of them.