There are many points of interest in the A Dying World 700AF area of the Historia Crux, including numerous Fragments, a Paradox Ending, a Wild Artefact, and even a few useful items.
First, seek out the Wild Artefact by heading to the Farseers’ Relic. Use Moogle Junt next to the Oracle Drive and examine it to start up a cutscene. A Live Trigger Event will occur. When asked, anser “I can do this.” A Wild Artefact will appear in front of you after the ensuing cutscene ends. This is the last Wild Artefact that you can collect from the game world. If you are still missing one and can’t get 100% completion, check the shop in Serendipity.
Now, move on to collecting the Fragments. There are three in this area, each of which can be found in a treasure chest. First, head to the Farseers’ Settlement area. This cleverly hidden chest floats inside of the well to the left of the building with the large white orb on top of it. Use Moogle Throw to retrieve the Ultima Brand Fragment from the well. Now head to the Abyssal Fissure area. This is where you will find the other two Fragments. The first, the Omega Brand Fragment, is located to the left of the Gate. It will be floating on a stone ridge. After picking it up, head south to the border of the Black Sands area. You’ll see a chest floating above a bridge of scrap. Use Moogle Throw to grab it. It will contain the Chaos Brand Fragment.
Next on your checklist should be the Paradox Ending. You will have to face Caius Ballad yet again, so keep that in mind as you reset the story progress in this area. Deactivate the Paradox Scope afterwards, then play through the story until you get to New Bodhum. Reactivate the Paradox Scope here. Keep going to get to the A Dying World area. Here, you must fight against Caius.
Boss Battle: Caius Ballad
Caius will be much stronger in this battle here than he was in the main story, but still not as tough as he was when you faced him for a second time with Serah alone. Caius will begin the battle by casting a quick and painful series of attacks. You, on the other hand, should spend this initial period turtling up and buffing yourself. Cast Vigilance first, as it can be especially helpful during this encounter. Once Caius’ initial flurry of strikes have landed and you have been sufficiently buffed, switch to the Saboteur Paradigm and use Deprotect on Caius. Once it sticks to him, switch to a Paradigm such as Tri-Disaster or Smart Bomb, one that makes heavy use of Ravagers. Use their magic to quickly build Caius’ Chain Gauge.
Once Caius becomes staggered, use the Cerberus Paradigm to mercilessly whittle his health away. Once his health reaches zero, which shouldn’t take too long, Caius will of course replenish it all and enter the fray refreshed. Don’t let this discourage you, though, as this boss is actually much easier to kill the second time around. He will not have the benefit of an initial flurry of attacks to catch you off guard. Instead, he will merely begin attacking as usual. Use the same strategy of buffing, casting magic, and using Commandos after Caius is staggered to fell the boss easily.
After defeating Caius yet again, you will be thrust back into the Historia Crux. From here, select the A Dying World ???AF location to begin a cutscene and with it the Paradox Ending. You will receive the Transcript: Heir to Chaos Fragment for finding this elusive ending.
This is the last of the major items in this area, but note that you can also obtain the Golden Chocobo monster crystal to the west side of the Dead Sands area, in a chest. This is the only location in the game that you can obtain this crystal. Note that you can also battle the Metallicactuar enemy here, especially in the Farseeers’ Settlement area, and that this is the best spot to add this elusive beast to your bestiary.