To become a Master Romancer for a species, you need to have seven of that particular species in the garden at the same time. For example, to be a master romancer for the Preztail, you simply need to have seven preztails in the garden at the same time.
The easiest way to do this is by using the hunter to fetch your pinatas until you reach 7, then sell them off and start on a new one. You can also buy pinatas from the pinata store. Buy 7, get your master romancer, then sell them off.
Flutterscotch variants (blue, green, etc) are all considered "species", so you can get 7 white flutterscotches from the hunter, change them into a different variant of flutterscotch and it will count towards the master romancer achievements.
This website is an excellent VP reference. It tells you how to attract various pinatas, how to create variants, how to tame sours, etc.http://pinataisland.info/
Addition from Reils y0
Good solution. To add to it, all the pinatas in the Paper Pets store count towards the achievement. So, you can buy 7 pinatas on the spot and then sell them all back for a slight loss. This is a less time consuming method than Gretchem's that can help contribute towards the achievement.