How do you beat the final boss in Zelda Wind Waker for Gamecube?
I'll assume you mean the fight against Ganondorf himself and not the many monster forms beforehand.
There are several steps to the battle:
1) Attack Ganon directly. As you finish your combo, press A to jump over him and get behind, then attack rapidly. Alternatively, have him come at you, and make sure Zelda is out of his sight; she'll hit him with a light arrow and stun him, allowing for you to inflict damage.
2) Ganon knocks Zelda out. Dodge his jumping attacks to the side as the game prompts to inflict damage to his back, or press A as you finish your combo when he's blocking to get over him.
3) Zelda wakes up. Keep on going...Ganon will probably block all attacks at this point. Eventually, Zelda will talk to you(or maybe you have to talk to her; can't quite remember). She'll ask you to reflect her light arrow with your mirror shield. Proceed to do so. Ganon is stunned. Walk up to him and press A for Link to finish the battle in a most gruesome fashion.
Video of the fiight:
I'm going to add a bit to @Mana's answer, in the off chance that you are referring to the shadow beasts that come immediately before Ganon.
The key to all 3 of them is to hit the blue orb that is the tail with an arrow of light. The method of doing so varies among the first 3.
The first guy looks like a puppet, with a long tail. Use your boomerang to cut each of the 5 strings. They are strong strings, it takes 2 blows to get them knocked down. Ignore the brown/reddish one in the middle, this is the string by which the beast is controlled by Ganon. When all of the strings are cut, hit the tail with the arrow of light. Repeat 3 times, and you'll hear victory music, followed by realizing the beast is going to come back.
The second time, it's a spider looking creature. Look up, wait for it to stop. When it stops, go to the area where the blue tail is. Hit it with your arrow, and repeat until dead.
The last one is a fast moving worm. There is no real trick to this mode, just hit it with the arrows as you can.
Periodically, bats will come. Use them to stock up on arrows, magic, and some hearts.
It is the toughest boss, unless you do this (you should have the FULL arrow capacity, and magic upgrade, but it is optional):
I did this, and I managed to beat Puppet Ganon, after only taking one heart worth of damage. It's a crappy strategy, I know, but it works.