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