There are no certain party members that you need to use, I used Cloud, Cid and Red XII. I highly recommend Cloud and Cid because of their Triple Materia Growth weapons, Apocalypse and Scimitar. I reccommend no lower than level 65. Using this strategy at that level I get consistent kills around 2 minutes remaining.

Characters loadouts:

Cloud
Weapon- Apocalypse (Materia Growth x3!!!)
Armor- Escort Guard (Mystile has better stats, but you don't want Cloud to evade too many attacks and Mystile has high evasion)
Accessory- Champion Belt (Stronger Attacks, Stronger Defense)
Materia- HP Plus, Counterattack x3, 2x cut(4xcut if you have it)
Limit break: OmniSLASH

Cid
Weapon- Scimitar (Materia Growth x3)
Armor- Mystile ( good defense and helps to evade some attacks)
Accessory- Toughness Ring ( Improves physical defense and magical defense)
Materia- HP Plus, W-Item, up to 3 other materia you wish to gain AP
Limit Break: Highwind or any that damages all targets

3rd character of your choosing
Weapon- Strongest Double AP weapon available
Armor- Strongest Available
Accessory- Circlet( improved magic)
Materia- HP Plus, Enemy Skill, and up to 3 other materia you wish to gain AP
Limit Break: Strongest available that damages all targets

Emerald Weapon's strongest attack is a retaliation attack for defeating all of his *eyes* at once, AirTam Storm: which is Materia spelled backwards. The attack is unblockable, and is 1111x the number of materia each combatant has equipped, so you want to use as little as possible, I limit it to 5, so that at most the damage done will be 5555 to each person, I suggest using less, but I did it with 5.

Make sure you have as many MegaElixers and Hero Drinks as possible (Use the W-item multiplication trick before you start this battle)

The battle is pretty simple.
Cloud uses 2x(4x)cut
Cid uses W-Item: MegaElixer and then Hero Drink on Cloud
3rd Party Member uses the Enemy Skill: Big Guard
Repeat, continuously unless Limit Breaks available.

Depending on the level of your counterattack materias Cloud will attack up to 3 times every time he is damaged. After a few Hero Drinks that is 9999 3x without even using your turn yet. When Cloud gets his Limit Break, use it because he is not doing anything else besides attacking every turn anyways.

Cid should always use a MegaElixer every turn (use the W-Item multiplication trick in a previous battle to make sure you have 99 before this starts) because you will likely be damaged before he gets to actually use it, so even if your health is full, still use it. Use Hero Drinks(again make sure you have a ton of them using the W-Item trick before you start this battle) on Cloud as the second item until Cloud is consistently hitting 9999, then you can start using them on other characters.
In the event someone dies use a Pheonix Down and then a MegaElixer.
If Cid gets his limit break, make sure another character is scheduled to use a MegaElixer before Cid attacks just in case Emerald severly damages anyone in between his limit and his next turn.

The Third character should use Big Guard every turn to buff your defenses and give you haste. One of Emeralds attacks completely erases one characters defense buffs so its always good to use it continuously. And use your limit break whenever you get it, unless Cid is also using his then in this case use a megaelixer to make up for him missing his turn to heal.

If you want you can give Cloud the Underwater materia in place of one of his counterattacks to eliminate the timer, but with 3 counterattacks you should be able to defeat him before the timer runs out.

If you do not break from the pattern of Attacking, casting Big Guard, and using MegaElixers and Hero Drinks this battle is cake. In the case of limit breaks Always remember to have a secondary megaelixer healer when Cid is using his limit break. There will be plenty of times where you are still fully healed and you "waste" a megaelixer but cloud's hero-drink-boosted damage output will make up for those wasted turns.

This is my first ever guide, so I'm sorry if it isn't organized efficiently
If you feel like there are any problems or slight errors please let me know and I will edit it.
Also if you have any suggestions from your own experience that would improve this guide I will be happy to add them to this.