To unlock Galax, complete a total of 100 laps on any race course in Air Ride Mode. Oh, and apparently Galax is another name for the course "Nebula Belt" Hope this helps.
For GameCube: ALL YOU DO IS ASSEMBLY THE THREE PARTS LISTED HERE.
Dragoon Part A. Jump over 1000 feet in High Jump Dragoon Part B. During 1 City Trial match, fly through 5 rings in the sky Dragoon...