Am I missing something? I need to heal every 2 or 3 turns because she hits so hard, and she heals from hitting me, so I can't deal enough damage consistenly to defeat her. And if she gets lucky, her crits just 1-shot me anyway.  Is there a strategy here? my best attempts so far have been with skill of the monkey (chance to counter) and Attack boosts.

Usually this combination of Star Knightess solves the problem:

• Protecting yourself
  • Protection of the Pig (Increase your DEF and MDEF)
  • Cry of the Rooster (Decrease enemy's ATK)
• Preparations for final strike
  
  • Bark Of The Dog (Decrease enemy's DEF)
  • Power Of The Horse (Increase your ATK)
  • Step Of The Rat (5 Normal Attacks instead of 1)
    
• Finishing him
  • Bite Of The Snake (Getting Tactical Advantage)
    
  • Attack

After 5 Crytical buffed-up Attacks against enemy lowered Defense usually it's enough, but you could repeat the last part again. The first part will drastically reduce damage from enemy. It's still possible if enemy gets Tactical Advantage but you could Guard on this turn.

Good luck