When you use X to throw a Frankenimpa towards an enemy it will cause a bit of splash damage to the enemy, providing the Frankenimpa comes in contact with the enemy before he stops. To get this achievement what you must do make sure the final hit is caused by this kind of damage.
The best way to achieve this is have a group of these in your party and throw a few at a time at the enemy. Once this has been done use B to recall the Frankenimpas back to you. When the enemies health is low launch several towards the enemy and if the last bit of damage is dealt by your thrown Frankenimpa the achievement will unlock.