My first thoughts on started Final Fantasy XIII-2 were: I have no idea what's going on.
Lightning is in Valhalla fighting a new enemy. There's an epic battle that feels like it belongs at the end of a game, not the beginning. It is given no context. Then a random new character is transported there through time and/or space and told to go on a mission to bring Serah to Lightning.
Then we cut to Serah who has memories of the events of at the end of Final Fantasy XIII. Unfortunately for her, most people don't remember it the same way. They all say that Lightning was never there at the end of Final Fantasy XIII.
After playing for the first few hours of the game it becomes apparent that timelines are mixed up and there are paradoxes everywhere. The game is structured around unlocking new timelines, traveling through time, and solving paradoxes.
It's not a bad premise, even though it's explained very poorly, but the gameplay doesn't do enough to differentiate itself from Final Fantasy XIII. In fact, the combat is identical to Final Fantasy XIII and that makes me very sad. I've already spent enough time with this Paradigm shift battle system. I never need to see it again.
That's not the only negative either. The game engine doesn't seem as smooth as Final Fantasy XIII. I'm playing on a very high-end PC and I saw a ton of slow down in the game. The cutscenes may be gorgeous, but the game engine stutters along.
So after playing for awhile I realized that this game just isn't going to hook me. I thought that maybe I would be able to complete the Lightning Trilogy if I just sat down and started on Final Fantasy XIII-2, but I feel like this game isn't worth my time. In the end I read a plot summary so that if I choose to try out Lightning Returns I have a little more context. Based on the plot summary, the story in this game seems all over the place.
I don't think I'm missing much by skipping it.
While I love Final Fantasy, and I'm willing to play through any mainline game, I won't slog through a spin-off game just because it has Final Fantasy in the title. Since I wasn't having fun with Final Fantasy XIII-2 it is time to move on.