Move forward and you’ll see Yeul, from now on you only need to talk to ‘every’ Yeul that appear on the map. You’ll obtain a new fragment automatically each time you have talked to her. The list of the fragments are:
You’ll fight Caius at the end of this dungeon. I believe you don’t need any specific tactic against him because he doesn’t have any dangerous attacks.
Talk with everyone you see and then go to NORA house. Go to Lightning who standing on the dock. You’ll be offered 2 choices on live trigger.
Choose yes first to obtain paradox ending and Transcript: Fate and Freedom Fragment. On the next game, choose no unless you want to see the ending one more time :D. Follow the voice that calling you (it’s on the meteor crash site). See an event…..
New area is unlocked
Follow Noel to wherever he goes and try to talk with him. Use moogle hunt to find Caius on the location shown in the screenshot above. You’ll fight Caius by using Noel (it’s also easy like Serah’s battle). You’ll obtain Martyr’s Emblem as a reward for defeating him. Now follow Noel to northwest of 10 Vitality Essences. See an event and
Recommended Paradigm: Tri-Disaster and Relentless Assault
After beating Gogmagog, you’ll see Live Trigger, I choose “I still want to change the future” and obtain Crystal Rose as a reward. From here you only need to go to point (1) on my map; it’s farseer relic, examine it to get out from dying world 700 AF.
 Don’t forget to take Golden Chocobo on cube treasure chest. It’s one of the strongest ‘commando’ monsters on this game.
 The west part of dying world can’t be accessed at this moment (red area on my map), so just ignore it for now.
 I don’t know whether all of the items that I have listed is available during your first visit to this world ( I obtained them on second visit).
 During this visit you’ll only get Gogmagog fragment beta ( don’t know whether ultima brand can be obtained now or not; chaos brand and omega brand are obviously can’t be obtained because you can’t go to the west side of this area). For specific fragment guide for this area visit this link.
 Strigol drop Segmented carapace and Garganzola drops Mutant extract. Both of the items are needed to create decent weapon on Chocolina shop (ATB charge +35% and Chain bonus Lvl 3).
PS: (1), (2), and (3) show fragment location, for the detail guide of the fragment. Visit this link
Go to the the golden timerift to see an event. Your moogle hunt will be upgraded, you can reveal advanced object now. Get map of the new bodhum 700 AF. Go northwest and take Artefact of the Ark. Head south to the gate (Historia Crux). This gate will end this episode and open Academia 500 AF on Historia Crux.