Quick Battle mode:
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Win the Pro AM Class in the World Racing League to unlock Quick Battle mode.

Quick Stunts mode:
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Win the World Racing League on the Easy difficulty to unlock Quick Stunts mode.

Time Attack mode:
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Win the Pro Class in the World Racing League to unlock Time Attack mode.

Pro Class:
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Win the World Racing League on the Easy difficulty to unlock the Pro Class.

Mach 6:
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Win the World Racing League on the Easy difficulty to unlock the Mach 6.