To ensure success, equip each party member with the best Materia: Final Attack linked with Revive, Mime, Restore, HP Plus, MP Plus, and at least one party member should have Knights of the Round, W-Summon, and Underwater Materia.
It is suggested that you have Yuffie, Cloud, and Tifa in your party with their Ultimate Weapons. Yuffie's Ultimate Weapon, Conformer, inflicts damage to the enemy based on the difference between her power and the enemy's power. Since the power between Yuffie and Emerald Weapon is so great, she will be a good person to bring along.
Tifa's Ultimate Weapon, Premium Heart, inflicts damage based on her limit meter. So, if her limit meter is almost full, she will hit way harder.
When you begin the battle, you may want to cast Haste and Regen on all your party members. Then, when you get a chance, W-Summon Knights of the Round which will cause about 200,000 damage points. After that, wait for Emerald to transform (three gems will appear on each of its arms) and then Mime with another character to cause Emerald to change again. Of course, Emerald will attack you. That is why you have the Revive linked to a Final Attack Materia. That will bring you back to life to full health by using Life 2.
Repeat the above process until Emerald Weapon is defeated. If your MP levels get low, use a Turbo Ether. One more hint, be careful when using Mime and make sure the last spell cast was Knights of the Round and not Life 2.
When you defeat Emerald Weapon, you will obtain the Earth Harp. You can give the Earth Harp to a man in Kalm for three Master Materia.