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