While you're busy destroying your brain to figure out the game's logic, you will at least have a beautiful environment to look at. Unfortunately, graphics alone do not make a game great.
My final opinion and score for this game really comes down to the audience. If you are a fan of Japanese pop culture, or you are an otaku yourself, you are sure to find something to love in this game.
...but for those who give it a chance, you'll find what I believe to be one of the best stories in video games of recent memory. Even if you have to seek it out on PSP, it is most definitely a game worth your time.
If you can deal with the game's difficulty, which isn't off putting but not exactly new player friendly, Abyss Odyssey is definitely a game worth a shot.