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