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Gogmagog Fragment Gamma - You get this fragment by defeating the boss. This is story related and you can't miss it.
Ultima Brand - This fragment is in a well in the Farseer settlement. If you are going N, it's just NW of the fork where the path splits. It's a well with a crane/pulley system just above it. You may have to back up some to get the correct angle on the Moogle Throw.
Omega Brand - From the NW Time Gate, this fragment sits in a treasure cube on a ridge to the SW and to the NW of the bridge leading to the next area. You'll have to Moogle Throw to get it.
Chaos Brand - From the NW Time Gate, head S and over the bridge (which is or was phased). Keep heading S from the bridge until you find a hill with a phased Treasure Cube and likely a Chocobo on it. Moogle hunt and open the cube for this fragment.
A Dying World -???AF-
Transcript: Heir to Chaos - You must get the "Heir to Chaos" Paradox Ending for this fragment. See the Paradox Ending section for more details.