Yuka Kazami and Medicine Melancholy both have 6,000 HP. Yuka has 0 Defense and 50 Magic Defense. She is weak to Lightning attacks and is immune to Earth attacks. Medicine has 200 Defense and 80 Magic Defense. She has no weakness, but she is immune to Light and Dark attacks, and heavily resists Earth attacks.
Recommended team: Sakuya, Marisa, Sanae, Byakuren, Patchouli, Aya as commander.
Sakuya should have 25 points in her Greatsword tree and 16 points in her Time Stop tree. She should be using Full Moon Revenge and Private Square.
Marisa should be using her strongest Lightning type attack (Stardust Surge (星屑怒涛), level 32, if you have it, otherwise Stardust Reverie) backed by Stardust Missile. She should have 20 points in her Astronomy points, with the remainder going in her Magic Mushroom tree. Marisa should be using the Bardiche (バルディッシュ, obtained from the magician fairy enemies in Stage 7) if you have it, as well as any other +Lightning damage gear.
Patchouli should be using Thunderbolt (サンダーボルト, level 27) and Active Elemental. She'll be AE'ing for Lightning. She'll need 16 points in her Magic Mastery tree, with everything else in her Spirit Mastery tree. Any leftover points that cannot be spend should be spent in her One-Week Girl tree.
Byakuren will need Elemental Weapon, Weapon Bless, and Spell Enhance. She'll need 25 points in her Support Magic tree.
Sanae will need Prayer's Wind, Sword's Wind, and Serpent Barrier (5point Snake tree skill). She'll need 5 points in her Snake tree, 20 points in her Spirit Magic tree, 10 points in her Youkai Extermination tree, and the rest wherever you want. The goal is to use Serpent Barrier on the very first turn to make sure that Medicine doesn't start her poison crap, so the +SPD bonuses will be useful.
Aya should have any number of bombs that result in a multiple of three. Points should be dumped into her Reporting tree.
A lockdown strategy will be used for the first part of the fight:
Turn 1: Aya commander bomb into Private Square. Sanae uses Sword's Wind, Byakuren uses Elemental Weapon with Lightning, Marisa uses a Lightning attack, Patchouli uses Active Elemental for Lightning.
Turn 2 and 3: Full Moon Revenge on Yuka.
Turn 4: Aya commander bomb, defeat Yuka with your lightning-property attacks. Sanae uses Prayer's Wind this turn, Byakuren uses Weapon Bless on Sakuya.
Turn 5+: Defeat Medicine, reapplying buffs and healing as needed.