The only tricky part about this achievement is getting your GEM count to a multiple of 50. This is not as hard as it sounds, however. Simply play the Brush Time! game from the toy box. If played enough times, each GEM that you win will always be reduced to one. Every time you keep the meter in the 'perfect brush speed zone', in the middle of the meter near the GEM icon, it will get you exactly one GEM every few seconds. Keep replaying this if needed to get a multiple of 50.
Once you have the right number of GEMs, go to the "Pet Database" in the smart phone menu as many times as needed to get your GEM count to zero.
Note: Playing Brush Time! will also count toward your "brush your pet for a total of ten minutes" medal (15 x 40 seconds = 10 minutes).