If you like Final Fantasy this is the latest one.
Final Fantasy XIII-2 begins three years after Cocoon's fall, noted in-game as 3 AF, as the Pulse town Serah lives in is attacked by monsters. A stranger named Noel appears to save the town, and claims to be a time traveler from 700 AF. He arrived in 3 AF via Valhalla, a realm at the end of time, where he claims to have met Lightning guarding the throne of the goddess Etro, who, according to myth, created humanity. As part of Lightning's transfer to Valhalla, paradoxes have erupted throughout time, enabling time travel between specific time periods via the Historia Crux and modifying history. Serah joins Noel to resolve these paradoxes: she hopes to find her sister while he hopes to change the bleak future from which he came.
They journey to Cocoon in 5 AF, where they meet Alyssa and stop a giant war robot from the future, and then move on to the Pulse Yaschas Massif in 10 AF. There they find Hope, now the leader of the Academy with Alyssa as his assistant, and they also find a recording of prophecies made by the line of seeresses of Paddra, believed to have died out centuries prior. One fragmented prophecy shows Lightning in Valhalla. The city of Paddra is shrouded in an eclipse, which Noel says is not supposed to happen for another few centuries. While Serah and Noel resolve the paradox, they encounter Caius, who Noel knows from 700 AF and who opposes them in changing the timeline; and also Yeul, who looks identical to a girl named Yeul that Noel knew in the future. After resolving the paradox, a new region opens in the Historia Crux, 1X AF Paddra, an alternate timeline in which there was never an eclipse in 10 AF. The prophecy now shows Caius in Valhalla fighting Lightning, as well as the pillar supporting Cocoon collapsing. Noel claims that this takes place around 400 AF, and devastates the world along with the human population, resulting in the extinction of the species by his own time. Serah and Noel move on, while Hope and Alyssa work on preventing the pillar's collapse.
In 300 AF Cocoon, the pair find Snow, Serah's fiancé, who disappeared while searching for Lightning. He is fighting a giant paradox-fueled monster that is dissolving the crystal pillar. After resolving the paradox, which delays the fall of Cocoon until 500 AF, Snow disappears again as an anomaly from another time, much to Serah's dismay. The pair then go to the city of Academia on Pulse in 400 AF, where they are attacked by the citizens transformed into Cie'th by the city's Proto fal'Cie, which claims they were killed in a tower in 200 AF after learning a "forbidden history". After the Yeul of that time dies, Noel and Serah go to the Augusta Tower in 200 AF, where they discover that Hope, in order to prevent Cocoon's destruction, made the Proto fal'Cie Adam in 13 AF to help keep Cocoon afloat. A paradox, in turn, caused the Proto fal'Cie's AI to lose control, kill Hope and Alyssa, and take control of the Academy. The paradox is resolved when Hope in 1X AF sees a prophecy of the pair fighting Adam and decides not to build it, creating an alternate Academia in 4XX AF. In this world, the pair find Hope and Alyssa again, who had put themselves in stasis after building Augusta Tower. They explain their new plan to build a new man-made Cocoon to hold humanity, which Serah and Noel help with before departing again.