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