The author uses the word "metamorphosis" to describe the "four-stage process of change." They are introducing new vocabulary terms in a friendly context. They also may have included it because it's the most accurate scientific term for the process of growth undergone by the beetle.
Stratigraphy is a part of geology that is worried about the investigation of rock (layers) and layering (separation). It is fundamentally utilized in the investigation of sedimentary and layered volcanic rocks.