Here is the full list of all 12 FurBalls Racing achievements.
Finish the tutorial
Finish the tutorial in less than 30 seconds
Earn a gold medal
Earn a platinum medal
Get 1st place in the Fuzzy Cup
Beat a staff ghost
Beat an expert staff ghost
Get 1st place in the Squishy Cup
Get 1st place in the Shiny Cup
Get 1st place in the Crazy Cup
Get 1st place in the Ultimate Cup
Hold right click or 'Y' while pressing 'OK' on the character select screen...