Here is the full list of all 14 Teddy Floppy Ear - The Race achievements. It takes around 5-6 hours to unlock all of the achievements on Windows.
Win the Large Cup.
Win all Collectors Slaloms to unlock this achievement.
Win all Time Attacks on nightly tracks.
Win the Medium Cup.
Win the World Class League.
Win all Time Attacks on daily tracks.
Win a Single Race on an Expert level.
Win all races in the Pro League.
Win all races in the Semi-Pro League.
Win all races in the Amateur League.
Finish a race without using any powerups.
Win a Single Race.
Win the Little Cup.
Use a shortcut on any of the tracks.