You need to enter the Red Painting. The one which was activated with the Staff of Hermes. In there you'll find yourself in the place you met Nelo Angelo for the 1st time. The elixir responds to the mirror, so enter it to go to another dimension. When you do exit the room through the window. Jump down to the place you fought Nelo Angelo for the 1st time. In the center you can see the Philosopher's Stone.
Note: After taking it prepare for some tough guys, I suggest using Ifrit.
Also welcome to the forum, why don't you offer an introduction as this is the Introduction forum?