The Palace of the Four Sword is an all-new dungeon exclusive to the Game Boy Advance version. To access it, fall off the far-right ledge of the pyramid and go into the hole. You must first have completed the Four Swords multiplayer adventure in order to be a "true hero" worthy of accessing it... unless you cheat. The 4 Swords Mastah Save includes a Gameshark Save with everything required for this dungeon already completed.
While you can enter the Palace as soon as you have beaten the Four Swords and have access to the Dark World, mostly finishing the game first is recommended as many items are required, and the more hearts you have the better. It's also advisable to bring four Red Potions (or just fairies if you prefer). The minimum items needed are the Hookshot, the Flippers, the Cane of Somaria, the Magic Hammer and the Fire Rod.
Anyway, head on in. Avoid the Chain Chomps and go into the next room. This central hall connects you with all four areas. First, go southwest.
The Green Sword
This one is the easiest. The water current is too strong to swim against, so light the torch first. Swim upwards. When cannonballs and the roller come your way you need to dive using 
. When you reach the door, enter it.
Boss: Arrghus II
First, Hookshot each jellyfish and kill it. Like other jellyfish in the game they randomly become electified; attacking them at this time will of course hurt you. You could also pull them away and then shoot them with the bow. Arrghus will try to ram into you, so you'll need to keep moving. Every now and then he shoots the jellyfish away in a wide spinning circle. This deals a fair bit of damage, so move out of the way when it happens. Remember that you're invulnerable when using the Hookshot, so a well-timed shot will allow the jellyfish to pass over you harmlessly.
When all his jellyfish are destroyed he'll jump up into the air and try to crush you. Move just as he comes down and slash at him. If you miss he'll swim around like crazy bouncing off the walls. During this second stage strange bubbles will rise and try to hit you, so slash them to destroy them. Nine hits from the Golden Sword will take him down. Go into the next room and pull the Green Sword from its pedestal, then step on the teleporter to return to the main hall.