To
unlock Flipendo you need to complete Professor Garlick's two assignments. Upon completing the side quest "
Professor Garlick's Assignment 2" you'll be rewarded with the Flipendo spell.
Now with the spell equip it's simply a case of tracking down some Cows and continually casting Flipendo on them, until the achievement pops. I found the most convenient place to find a Cow was
just south of the "East Hogsmeade Valley" Floo Flame. You'll find three stood in front of a pop-up carnival tent owned by "Leopold Babcocke" who is also visible on the world map.