This achievement is called Cat Mania.
Summon the giant KapuKapu and gobble up Big the Cat for mouse revenge!
RIght, what you have to do is buy the ChuChu Pilots. They are pretty expensive, they were 25,500 SEGA Miles (cheers Mikey B).
Right then you start a single race and change it to 5 laps. Pick the ChuChu's and start on any track. Make sure the Big Cat is there (You may have to buy him first but I don't know as I already had him) If he's not there exit and try a different map. Right when it's set up stay at the back of the pack until you get the all-star move which looks like a chu-chu cat thing which is orange. Once you have it try to hit the Big Cat. If you miss just restart the race as the racer's stay the same. Do not exit as next time the Cat may not be there.
Hit him once and bam Achievement Unlocked. You can now quit or carry on fr SEGA Miles and the ChuChu win :)