Marso1's solution is definitely the way to go. However, the biggest issue is knowing when to start attacking in mouse mode. Risky Boots has a lot more HP than I expected. Guessing was getting me nowhere so I got to testing.
As far as I can tell, Risky has EXACTLY 2000 HP.
The smartest method, as long as you have the magical tiara, is to hit her with Obliterate 79 times. This will leave her with only 25 HP. Then switch to mouse mode and finish her off. You could whip her three times with fully upgraded hair, leaving only 1 HP, but no reason for unnecessary risk at that point in my opinion.
If you don't have the tiara it'll be more bothersome to count. That's 249 whips with fully upgraded hair before taking down the final 8 HP with the mouse. More annoying but still manageable if you can keep count.
If you screw up, a dashboard and reload will take you right back to before the fight.