You can only fight the Enigmatic Man (the Unknown) in Kingdom Hearts: Final Mix, but if you do have Final Mix (which you said you did), you have to seal all the Keyholes (excluding 100/Hundred Acre Wood) , get all 99 Dalmations, complete the Hades Cup, and activate all the Trinty Marks. Then go to the End of the World, and leave (not sure if this is correct, but I'm pretty sure it ia). Go back to the Chapel in Hollow Bastion and there should be a portal leading to the Enigmatic Man/Unknown.
If you're playing Final Mix on Proud Mode, you just have to get all 99 Dalmations and activate all the Trinity Marks (not sure if this is correct either, but I'm still pretty sure it is).