How do you identify archetypes in a story?
An archetype is the purest version of a common sort of stock character.
Some of literature's best characters have come from its worst writers. Great writers avoid archetypes, while lesser writers use them without hesitation. An archetype isn't necessarily the best version of a character type, but it is the purest, and therefore the least challenging for a reader.
James Bond is the ultimate spy. He wasn't literature's first or best, He is devoid of features that make him realistic or non-stereotypical. Giving him an interesting flaw or a memorable trait might dilute the quality that makes him more marketable than a better-written character. Mike Hammer is the ultimate hard-boiled detective, replacing Sam Spade, who was more interesting and less pure in concept and execution. Tarzan was preceded by Mowgli and by Rousseau's "natural man," but who are you likelier to see on a lunch box or as a Halloween costume?
If you look at a specific character, ask yourself: Is there a better-known version of this particular type? Does this character have any distinctive traits that distract from his or her shtick ? Are there subsequent characters obviously influenced by this one? If the answers are no, no and yes, there is a good chance that this character is an archetype.