In addition to the hard-shelled eggs, what characteristic of a fish would have been very helpful to the first fully terrestrial Reptilia?

Uh, hard-shelled eggs aren't particularly a characteristic of fish, so this is a bad question from the get-go.

There's no firm dividing line between a taxon and its immediate ancestor, so there's really no "first fully terrestrial Reptilia."  The early reptile probably inherited scaly skin, limb muscles, pointy teeth, lungs, three-chamber heart, better brain, and claws from its proto-reptilian semi-amphibian ancestor. 

So -- nothing's needed from fish.  Your silly teacher might want "scaly skin."  "Scaly skin" isn't a defining characteristic of "fish" anyway.

Well, you can believe that God did it during the seven days He created the earth fitting in all of the evolution at the same time.