How do you get the secret world on Kingdom Hearts 2

There is no actual secret world in Kingdom Hearts II. The only world that becomes revealed as you reach the end of the game is The World That Never Was, but it is hardly secret as you need it to finish the game.

Considering the "secret" portions of Kingdom Hearts II, there is:

-The fight with Sephiroth (the hardest boss of the game) in the Dark Depths of Hollow Bastion/Radiant Garden. (Do not fight him unless your levels are good and you've maxed out a few forms. Take this from someone who cares about you.) After fighting Sephiroth, you get to watch Cloud try and vanquish him, and Tifa gives you Fenrir, the strongest Keyblade in the game.

-The Paradox Cups in Olympus Coliseum, which you see Hades to enter the Pain and Panic Paradox Cup after beating Xemnas' first form, before you enter Kingdom Hearts in The World That Never Was to end the game. In order to get to the final Hades Paradox Cup, all of your drives and summons must be at Level 7.

-The Ultimate Keyblade, which is obtained through Item Synthesis (you got to love those Moogles), along with Save the King for Goofy, and Save the Queen for Donald. The process to get these is incredibly time consuming, but it is indeed worth it, as Ultimate gives you a tremendous advantage in fighting Sephiroth. However, you can make do without it.

-The secret ending movie is the last thing (to my knowledge) that's hidden about Kingdom Hearts II. Spoiling it for you would just be wrong, but you can only obtain this movie in one of two ways: If you are playing the game in Proud Mode, you have to seal all of the keyholes, or, if playing the game on standard, you must get 100% completion on Jiminy's Journal. That's the only way to get the movie.

I hope that this was helpful to you in some way.