Final Fantasy VII Guides and Walkthroughs
Emerald Weapon is one of the two super bosses in Final Fantasy 7, the second being Ruby Weapon <Add Link>. You can first challenge Emerald Weapon on Disc 2 after getting the Submarine but it's recommended you wait until much later when your characters are much better equipped and higher level.
In order to defeat Emerald Weapon you'll most likely need the Underwater Materia which is given to you by an old man in Kalm during the Kalm Traveler Side Quest. This quest requires you to defeat both Emerald and Ruby Weapon, for doing so you'll be rewarded with a Gold Chocobo. A pretty underwhelming reward for this point in the game.
Without the Underwater Materia you'll have a 20minute time limit while fighting Emerald Weapon which may not be enough time for you to defeat it.
Emerald Weapon Strategies:
Most Common/Easy Strategy: W-Summon + Knights of the Round paired with MP Turbo (to make things even easier use Mime on another character to repeat this)