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 Little Cup.
Win all races in the Amateur League.
Finish a race without using any powerups.
Use a shortcut on any of the tracks.
Win a Single Race.
Win all Collectors Slaloms to unlock this achievement.
Win the Large Cup.
Win the World Class League.
Win all Time Attacks on daily tracks.
Win all Time Attacks on nightly tracks.
Win all races in the Semi-Pro League.
Win all races in the Pro League.
Win the Medium Cup.
Win a Single Race on an Expert level.