You will need 43 total pets unlocked for this achievement. They are viewable in MY DEN - so count what you have and subtract what you need.
Remember, you can buy/earn gems then UPLOAD your save to the cloud, buy stuff, then DOWNLOAD your save and keep the gems you had... You will lose your unlockable progress though, so this strategy is best left for the end of the grind when you know how much you need to pop the achievement.