Following the first piece of advice, I started on Easy difficulty and headed to the upper city, captured it, defended against the initial attack, and then made a swift march to the second enemy city. I captured and converted it as well. I defended the upper city for quite a while; it's not necessary to kill everyone there. Right now, only one hero is roaming the surface; I'll take him out, then capture five portals, and after that, I'll leisurely search for the pieces of the Shanti-Imi disk. In this mission, it's important not to rush, but also not to dawdle.
P.S.: Dark Elementals are quite helpful. By the way, read the advice in the Conflux spheres – they often offer useful tips.