Find a nice long bit of shallow water and lure an animal to one end of it, preferable the end that makes it you have the maximum space possible between your end, and the other. Get all defenses up and attack until it has no defenses up. Attack until it flees. Since it's in shallow water, you can boat up to it and continually attack it until it dies. I killed my first badger this way.
You can also use this technique to easily earn CDs. I got artful evasion and steal thunder along with some moves i already had just from trying to kill the animal.