A pretty straight-forward follow-up. The finale of the first film set up the story for the sequel, so it's best to watch both Parasyte films in order. I guess it's not impossible to jump right into the second part, after all these films aren't that complex to figure out, but you're sure to miss some finer details.
Yamazaki picks up where he left off, which is with half-human, half-parasite Izumi on his quest to stop an alien invasion. With Goto (played by Asano, introduced at the end of the first film) there's a new and stronger adversary for Izumi, who in his turn gets help from Uragami, a questionable serial killer able to single out infested humans.
Like the first part, part 2 can get surprisingly gory and twisted, though never in a very sleazy way. Monster designs are interesting, the CG is decent and the cinematography looks polished. Yamazaki is a capable blockbuster director, even when the material is not all that blockbuster-friendly. Had a lot of fun with one.