Flipendo will unlock after completing Professor Garlick's Assignment 2. First, grow and harvest Fluxweed in the Room of Requirement. Then make sure you have a few of each of the combat plants. Find a small group of enemies in the open world. While fighting them, use a Chinese Chomping Cabbage and a Venomous Tentacular. Then, finish it off with a Mandrake. Return to Professor Garlick to learn Flipendo.
Once you have the spell, locate cows in the open world (there are some just south of the East Hogsmeade Valley floo flame next to the traveling vendor). Cast Flipendo on one of the cows 10 times and the achievement will unlock.