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