Life cycle is a compound noun which is also the subject of the sentence. The predicate is "consists of", which is a verb phrase.
The subject of the sentence is the compound noun life cycle.
The simple predicate is the verb consists.
The complete predicate is consists of 11 months.
The subject of a sentence is what the sentence is about: the entire life cycle of insects.
The predicate is the verb and all the words related to that verb that follow it. A sentence can have more than one predicate.
Note: The subject of the sentence is singular (life cycle), a thing spoken about (third person). The correct form of the verb is consists.
Also note: The noun insects should be the possessive form:
- The insects' entire life cycle... (plural possessive); or,
- The insect's entire life cycle... (singular possessive).