You can either find the Sprint Shoes or make them. One of the methods to
making them is using a Tetradic Tiara. Follow the order below exactly.
This method works best if you have the accessory that makes you more
likely to get a drop after a battle. Make sure you upgrade it to the top
tier as well.

1. Buy Four Iron-Bangles (500 Gil each)
2. Make sure there are no Tetradic Tiaras in your inventory.
3. Keep doing Mission 7 (Disc 3, Gran Pulse) until you get a
Tetradic Tiara (rare drop).
4. Save the game.
5. Break down all four Iron-Bangles.
6. Upgrade Tetradic Tiara level 1 to Tetradic Tiara ? (only one
level until star).
7. Break down Tetra Tiara ?.
8. Repeat these steps as many times as desired. 

The result should be one raw material that sells for 12,500 Gil, three
Talisman, and one pair of Sprint Shoes. The same process works if you
get the Tetradic Crown drop instead of the Tiara; however, instead of
breaking down four Iron-Bangles, just break down three. Also, instead of
getting the Sprint Shoes, you will get Herme's Shoes. If you upgrade
this to the star level (just one level), then upgrade it with the
correct crystal/stone/etc., it will turn into the Sprint Shoes.
Alternately, you can upgrade the Tetradic Crown to star level, then
using the correct stone/crystal (Mnir Stone or something similar), you
can turn it into Tetradic Tiara, and then perform the process above.