First
Make sure that you have the weapons with the most slots and the highest materia growth rate equipped. Also equip your best armor (I recommend the Mystile armor because it cuts magic damage in half).
Second
Equip the character with the highest magic levels (normally, this would be Cloud) with the following materia:
Mime (required) paired with Counter (optional)
Phoenix (required) paired with Final Attack (required)
*HP Plus (required - you need to have 8000 HP at least)
*Magic Plus (optional, but highly recommended)
*Speed Plus (optional, but highly recommended)
* (You may want to equip more than one of these to maximize the effect - also you'll want each of these materia at high levels, especially the Magic Plus materia)
Third
Equip the character whose magic levels are closest to those of your strongest character with the following materia:
Knights of the Round (required) paired with HP Absorb (recommended)
Bahamut ZERO (required) paired with Quadra Magic (recommended). PLEASE NOTE: It doesn't make any sense to use this combination at all if your KoR materia is already Lv. 3 or above!
W-Summon (required)
*MP Plus (optional - you need to have 700 MP at least)
*HP Plus (required - you need to have 8000 HP at least)
*Magic Plus (optional, but highly recommended)
*Speed Plus (optional, but highly recommended)
Mime (optional if you have a 2nd Mime materia) paired with Counter (optional if you have a 2nd Counter materia)
* (You may want to equip more than one of these to maximize the effect - also you'll want each of these materia at high levels, especially the Magic Plus materia)
Forth
Equip the remaining party member with HP Plus in order to bring his/her HP to at least 8000.
Fifth
Give the Underwater independant materia (you get it from the old man in Kalm) to any of your three party members to disable the 20 minutes time limit when you fight Emerald Weapon. Then you should fill all remaining free slots with materia you want to grow (you'll get LOTS of AP from this battle). You should also equip a "Choco Feather" or even better "Sprint Shoes" (you can get these at Gold Saucer by winning chocobo races - they are much more effective than Choco Feathers) on the character that holds on to the Mime materia (highly recommended) and the one who has got the Knights of the Round materia (optional, but recommended). Finally, you should put all party members in the back row and make sure they are healed to max. Save your game, so you don't need to do all of the above things again if you fail.
Sixth
You're now ready to attack the Emerald Weapon. Right after the battle starts, select "W-Summon" and cast "Bahamut ZERO" and "Knights of the Round" (if your Knights of the Round is already Lv. 3 or above, cast KoR both times instead). Then, use "Mime" continually to repeat the spells - you MAY NOT enter any other command than Mime! If a character is in turn who doesn't have a Mime materia equipped, simply skip him/her - that character will be useless in this battle. Keep using "Mime" until Emerald Weapon unleashes "Taire Air Storm", which will hit your ENTIRE party for 9999 HP damage. Altough this attack misses a single party member sometimes, your entire party will almost certainly die, but you will be resurrected by Phoenix. Then select W-Summon and cast Knights of the Round both times (if it only hits once, don't worry - when you Mime it, it will hit twice. Keep using Mime until Emerald Weapon dies.
You'll get the Earth Harp when you win, the old man in Kalm will give you all Master Materia in exchange.
Ruby Weapon Strategy
Here's a way to defeat the Ruby Weapon hiding in the deserts surrounding Gold Saucer - this thing has over one million HP! First, equip your strongest character (normally, this would be Cloud) with the following materia:
Mime (required) paired with Counter (optional, but recommended)
Knights of the Round (required) paired with HP Absorb (highly recommended - this way you will be healed to max each time you attack.
W-Summon (required)
*MP Plus (optional - you need to have 700 MP at least)
*HP Plus (required - you need to bring your character's HP to at least 8000)
*Magic Plus (optional, but highly recommended)
*Speed Plus (optional, but highly recommended)
Revive paired with Final Attack (optional, if you have enough materia slots free - this will revive you if you die, but will only be of use if Knights of the Round is already Lv 3 or above!)
* (You may equip more than one of these to maximize the effect - also you'll want each of these materia at high levels, especially the Magic Plus materia)
Then, make sure your character is healed to max and that you have your best weapons and armor equipped (I recommend the Mystile armor because it cuts magic damage in half). You should also equip a "Choco Feather" or even better "Sprint Shoes" (you can get these at Gold Saucer by winning chocobo races - they are much more effective than Choco Feathers), and you should put your character in the back row.
Go out in the field (don't attack the "Ruby Weapon" yet!) and engage in random overworld battle. During the fight, kill your other party members with your powered-up character (this is IMPORTANT since the "Ruby Weapon" otherwise will randomly choose two of your characters and kill them, so in any case you would only have one character left). Save your game (so you won't have to do all of the above things again if you fail), then attack the "Ruby Weapon".
Right after you engage in battle, Ruby should bury his claws in the sand. After the giant tentacles popped out of the sand behind you, immediately attack them by W-summoning "Knights of the Round" two times (be sure to target the tentacles and not the main body!!). This should kill the tentacles instantly. When you are able to select commands again, use "Mime" to repeat your spell. If Ruby Weapon sticks its claws into the dirt again, move your cursor to "Mime" while the tentacles are not yet visible, and push the O button ONCE (!!) (you should see a small blinking hand with a red cross through it next to your character). Wait till the red cross disappears from the tiny hand, then press the O button again (this procedure will make sure that your character targets the tentacles and not the main body - which is important since the tentacles can be a real pain, so you should kill them instantly when they appear. If this does not work, it's not that worse, though). If Ruby attacks, simply use "Mime" and you will be healed to max when your spell finishes. Keep using "Mime" over and over until Ruby Weapon dies (remember to proceed as described above when Ruby buries his claws). When you win, you will get the "Desert Rose" which you can give to the old man in Kalm. He will give you a Gold Chocobo in exchange.
Happy waiting! (Knights of the Round repeating over and over takes some time...
