Question

What is the function of the noun phrase "One of the largest insects in the world" in the sentence?

Answer 1

The noun phrase one of the largest insects in the word is used as predicate nominative in this sentence. If it is easier for you, just invert the places of the subject (the Goliath beetle) and the predicate nominative (this whole phrase) and it should be easier.
A predicate nominative is the first noun following a linking verb such as to be (or here is).