An extremely consistent guide on how to defeat esix since I've noticed some people have a bit of trouble:
1) Get 2 Silent Flowers from Icy Tops
2) Make sure you've picked up all the Catnips and Lemon Pie from Game Oasis and Pokemon Lagoon; you can visit the characters and they will not be there, but there are some items for you to pick up, you just need the Catnips from Rosie/Nyancy and the Lemon Pie from Brownie/Madea (Gracie gives you wood and rope which isn't helpful since you won't be using the heal at all if you follow this guide, and Fia doesn't have anything at all)
3) Go back to Northern Ruby Island, talk to Puck and get the Golden Piercing, you will need Puck's Wrath
4) Spam Sweet Tooth, then Feline Energy when Sweet Tooth runs out, do not use the heal at all, and the only two attacks you should guard against are Freeze Beam (using the Sapphire) since that has a chance to stun you, and Charge (using the Ruby) since it nullifies your attacks that turn anyways; otherwise just trade blows with her using Sweet Tooth/Feline Energy
5) Once you get her at/below 50% HP, the next turn she will always attempt to use Recover or Meteoric Rain, use Silent Blast this turn > Puck's Wrath next turn > Silent Blast the turn after that