On the 50 F, see the map to know the exact location.
Obtained by solving the timerift puzzle that appears after completing all of the side quest on Yaschas Massif 100 AF. Visit this link to learn more about Yaschas Massif 100 AF sidequest.
The fragment is located on the west side of Archylte Steppe, so you need to able to jump higher (anti-grav jump) or have found the golden cactuar. The fragment’s location shown on the screenshot just take a look at it (need a moogle throw).
Located north of 550 Gil treasure sphere. Visit this link to see overall map. Need a moogle throw to obtain it
You’ll obtain it as a reward by completing Iridium Ring. See this link to know detail info about the fragment.
Exchange your Coins on Chocobo race building for 7500 Gil (equip bargain hunter skill).