The latest Challenge Event for Final Fantasy Record Keeper is called “Fang’s Oath.” It started on January 14th and will end on January 23rd 2016.
During this event you’ll be able to recruit Final Fantasy XIII heroes including Lightning, Fang, Sazh, and Hope (you’ll get a Greater Growth Egg instead if you already have them), and also find their Memory Crystals. You should also look out for Lightning’s Memory Crystal II in the upcoming + dungeon.
Further, if you accept the quest “Complete Lake Bresha 1 Classic (XIII)” you can recruit Vanille. And by accepting the quest “Complete the Hanging Edge (XIII)” you’ll also be able to recruit Snow.
Finally, the new ability added is the 2-star Lightning Jump. It’s a Dragoon type and sees your character leap into the air and then deal moderate lightning damage upon landing.