It's honestly my least favourite game of the XIII trilogy. I really didn't like the world structure at all. A lot of areas were kind of re-used from XIII which was pretty dull, and honestly not too much of an improvement on the linearity stand point. Plus each area then was often re-used again inside the game since you go there at different points in time. To add insult to injury it wasn't exactly very open either, so you couldn't just skip the worlds which were boring, you had to often go through a world to unlock another world and then eventually you'll unlock the world you actually wanted. I preferred XIII's linearity to it honestly, XIII-2's just felt incredibly tedious. I'm glad LR just went with a more traditional open world with 4 "hubs", while I have a lot of complaints over LR, the world ain't actually one.
The story was mostly a load of rubbish since it was added onto a retconned ending of XIII. Noel and his friends had a decent story in isolation, but it was completely marred by all the time travelling, and also the general plot of XIII rearing it's ugly head.
I can't say I enjoyed the monster capturing either really.
I dunno I did really want to like it, but I just couldn't. By the end it felt like I was forcing myself through it just so I could get to LR and give it a try without feeling lost story wise. Considering the story in LR is pretty bad and nonsensical too, I really probably didn't need to. At least I did enjoy LR as a game more though...