Two player Team Battle mode:

Collect 20 emblems in single player story or challenge mode.

Two player Special Stage mode:

Collect 40 emblems in single player story or challenge mode.

Two player Ring Race mode:

Collect 60 emblems in single player story or challenge mode.

Two player Bobsled Race mode:

Collect 80 emblems in single player story or challenge mode.

Two player Quick Race mode:

Collect 100 emblems in single player story or challenge mode.

Two player Expert Race mode:

Collect 120 emblems in single player story or challenge mode.

Credit goes to "Lemmy"