Earth Eater: fortune spheres
Greater Sphere: luck spheres
Luck increases things like critical hit rate (and, if I'm not mistaken) rare steal %. Also, apparently, after reading some of the other threads, with 255 luck you only need base amounts for accuracy and evasion.
Right now, in my current file, I'm about to start collecting stat spheres from the species creation monsters, and eventually try out that 255 luck...I know it's gonna be a long road.