Whoo! I finally did it! It was 1:30 something in the morning and I was just at the "whatever" point, and I got to the end of the chocobo race with 0:0:00 and thought I had gotten it exactly because she gave me an elixer... until she preceeded to give me the sun sigil. I go "yaay" but was so tired it kind of didn't feel real... so I saved my game, and one minute later the power goes out.
Good timing. Make sure to always save your game I guess it was my house's way of telling me "okay you got what you wanted, now get some sleep!"