When an anime serves as a prequel for an Android-based RPG you've never heard of, chances are good that one shouldn't go into this series expecting much more than a four-hour commercial for the game it's advertising. Throughout the entire run of Zettai Bouei Leviathan, the show never really tries to be more than it is, which is a mediocre piece of fluff that just happens to have a fantastic voice cast.
Granted, the story is mostly non-existent, but to be fair, If you decide to watch this, you're probably not here for the story. For the majority of the show's run-time, the characters just sort of hang around and do nothing, with the occasional cgi bug battle thrown in. However, for the most part they just go to the beach, eat, or visit a hot springs. Additionally, this anime acts as a prequel to the game, so the plot doesn't even really kick in during the show. In other words, if you want a story, I'd suggest looking elsewhere.
As far as the characters go, they unfortunately don't fare much better. The cast mostly consists of the four main characters; Leviathan, a timid water-user, Bahamut, a selfish fire-user, Jormungandr, an adventure-loving warrior girl with an ax, and Syrop, a useless fairy that isn't good for anything other than food jokes. There's very little depth to the characters, who are best described as vague, color-coded archetypes. Although there is a bit of character development here and there, there isn't enough of it to make the audience care about any of them. So, this might not have a second season if you are hoping it will.