If you know how to beat him, Emerald Weapon won't stand a chance. All you gotta do is keep a few things in mind:

1. Emerald Weapon will only use Aire Tam Storm with at least 1 eye still alive.
2. Knights of the Round are very likely to kill all eyes in one turn.
3. With at least 1 eye alive, Emerald Weapon will counter all attacks with Revenge Stomp, and Knights of the Round (if it doesn't kill the eyes) with Aire Tam Storm.
4. Emerald Weapon follows a strict order of attacks, there are only two percentage chances in it. (One 2/3, one 4/5) If the percentages don't fail, Emerald Weapon will summon his eyes in the fourth round and use Aire Tam Storm in the eigth. There are ALWAYS three rounds between Eye Summoning and Aire Tam Storm (Eye Beam, Nothing, Eye Beam) unless you kill the eyes or Emerald Weapon gets angry (Happens when Revenge Stamp is used 10 times, Emerald Weapon's HP fall lower than 50% or Knights of the Round is used, possibly there's another way).
5. Emerald Weapon merely halves, not nullifies gravity damage.
6. Knights of the Round can be combined with HP or MP Absorb, but not with Quadra Magic (unless you're playing the PC version??).
7. Mime will mime 'every' attack, even limits, but only the user's, without any MP cost. 2x Summon + Knights of the Round -> 2x Mime anyone?
8. Although the Underwater materia removes the countdown, using point 7 will result in a kill with 10+ minutes left.
9. You can enter the battle with a Lucky 7 to deal 497728 damage (that's almost half Emerald Weapon's HP!) instantly.
10. Omnislash, Highwind, Ungarmax and End of the Living (can't translate it^^) can deal massive damage, so MIME THEM!

Edit: About the Cait Sith Limit, it's called "Game Over" and will work on any enemy (except zombies?) as it inflicts death status and ignores stat defense. You can get the first two reel slots with a bit of training easily, but the third one is based on luck, as you might also get a BAR and die instantly.