Adel will frequently drain HP from Rinoa. She uses a host of powerful spells; first she will drain HP from Rinoa, then blast a character with Flare or Holy. Her Energy Bomber attack is a physical hit against one party member that can deal high damage if Vit is low. When "Magical powers are concentrated on Adel!" appears on the screen, her next spell will be Ultima that can do up to 3,000 damage, but its damage is halved by Shell.
It is best that the player cast Regen on Rinoa at the start of the battle, followed by Shell, and be sure to Regen and Shell the party as well (Quistis's Mighty Guard works wonders). Rinoa has Regen spells to draw, which can be used for this purpose. Adel will frequently drain health from Rinoa, so one of the party should have the Recover command to occasionally top her up.
The player shouldn't use any multiple-target attacks in fear of hitting Rinoa. This rules out GFs and most Limit Breaks, especially the Renzokuken, because while it can deal a ton of damage to one character, some final attacks hit both Adel and Rinoa. Squall and/or Selphie should serve as the healers, topping up Rinoa's health and protection. The player is free to use Zell's, Quistis's and Irvine's Limit Breaks; for Zell's, the player must not activate the finishing moves; for Quistis, the player should use Homing Laser, Gatling Gun, Laser Eye, or Acid; Irvine can use any ammo except Shotgun and Fire Ammo.
A quick way to win the battle is to use Cactuar's Kamikaze command that will likely kill Adel in one hit, depending on the character's current HP. If this method doesn't kill her, it should still cause significant damage and she can easily be killed from this point.