Turns out a worthless Goddess saved everyone at the end of FFXIII and by doing so, doomed the time-space continuum because she wasn't supposed to interfere in the normal realm. She makes Lightning - who blatantly deus ex machina'ed her way out of her fate in FFXIII - her new vassal *ahem* Warrior Goddess.
Lightning then sends new guy Noel and Serah off on a journey to "resolve" paradoxes in time all thanks to the aforementioned worthless Goddess being such a shit deity. They encounter new baddie Caius who would like nothing more than to completely stop time so everyone's favourite South Park Kenny of the trilogy - Yeul - can stop dying over and over again because seeing the future kills her.
Old Cocoon due to fall and ruin the planet at some point hundreds of years in the future. Hope, who has inexplicably become a genius scientist and head of research finds a way to build a new Cocoon which involves hibernating himself for hundreds of years. Noel and Serah "stop" Caius, but Caius forces Noel to stab his heart. It turns out the aforementioned worthless Goddess decided to plant her HEART inside our baddie because...reasons. As Caius "dies" (hint: he's back for LR), so does the Goddess. Which means this essence called Chaos from that unseen realm she has resided in is unleashed onto the world, corroding it and contorting it into LR's new Nova Chrysalia.
Serah dies because for some reason or another she could also see the future which kills her because...reasons. Lightning in Valhalla while still being the worthless Goddess's slave, realises that Serah would die and kind of acts horrified, choosing to crystallise herself and...I dunno. I stopped paying attention there. I don't know anymore. =(
Oh, forgot to say. Fang and Vanille rescued from pillar just before Old Cocoon falls.