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 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 Amateur League.
Win all races in the Semi-Pro League.
Win all races in the Pro League.
Win the Little Cup.
Win the Medium Cup.
Win a Single Race on an Expert level.
Use a shortcut on any of the tracks.
Finish a race without using any powerups.