After exiting the Iifa Tree, make your way back to the Mountain Path and enter it once more. Go south once inside and take the right path this time, opting for the larger root to return to the world map near Madain Sari. Enter the town once more and once the scene is over, follow Eiko back to her home. Before you make a move, though, let's equip Zidane for an upcoming battle. If you never had the Power Belt on him and still have it in your possession, equip it now and put on the Counter ability. Stack him with defense and outfit him with Man Eater, plus Auto-Haste (of course) if you still have points available.
Enter Eiko's home and head to the kitchen, where you should see the moogles congregating around a hidden doorway. Go inside and watch the scene, then loot the two chests in here for a Survival Vest and Phoenix Down. Double back to the main portion of town and head north, which is where the Eidolon Wall will be, if you remember. Approach the entrance and you will have Morrison present you with a few options, like healing you. Peek inside after that and you will be given an Exploda and Elixir, before see a new option from Morrison. This doesn't pan out as expected, which leaves you with one more option to go save Eiko. Watch the somewhat lengthy scene, then you will be in a solo battle with Zidane.
BOSS - Scarlet Hair
While the normal battle music is playing here, this will be treated as a boss battle. The Scarlet Hair will do nothing but physical attacks on Zidane, usually hitting for around 150-200, depending on his defenses. He's also pretty fast, so the boss can pile on the damage quickly, so keep tabs on your health at all times and don't be afraid to use a Hi-Potion if it dips below 500. Once you hit Scarlet Hair, he will likely dance around the battlefield, which increases his evasion by a lot, so avoid trying to attack him while he does this. Whenever you see "Here I go," is when he will return to attacking you, so that's your chance to reciprocate the hits. Keep attacking when you have the chance, as well as keeping your health up, to easily win this battle.
When you've won, the Scarlet Hair will eventually retreat and you will regain control. Return to Eiko's house, to the very room where the item was first stolen, and watch another scene there. This will end up with you receiving the Memory Earring and Dagger will run off again. Exit Eiko's home and on the landing right in front of it, you should see an icon. Check this out to initiate a few scenes and as the party goes to leave, the Scarlet Hair comes back. This time, though, he will join your party and his default name is Amarant. At this time, you will have to choose your party, since you can only have four at a time.
Zidane cannot be taken out, leaving you with three choices. Vivi should stay, as his magic is extremely useful, leaving you with Dagger, Eiko and Amarant. Amarant is another physical attacker and having another of those will help, so you are left with choosing between Dagger and Eiko. Of the two, Eiko is a better white mage and has some more useful spells, although Dagger is the better summoner. For the purposes of this guide, the party will be Zidane, Amarant, Vivi and Eiko. If you decide to bring Amarant along, make sure you equip him with the Poison Knuckles you can purchase from Morrison, as well as any armor/accessories. The next stop on your adventure is the Iifa Tree once more.