He [...] nervously begins to scale the faces of the buildings. (11-13)
The Man-Moth clearly has some level of scruples, since scaling the face of buildings should definitely conjure up some anxiety.
He trembles, but he must investigate as high as he can climb. (16)
Folks don't usually tremble if they're just a little scared. This is bone-deep terror, and having no choice but to do it isn't helping much.
he climbs fearfully, thinking that this time he will manage (19)
What is he fearful of here? The task or succeeding at it?