'archetypically' ultimately derives from Greek elements via English. It is formed from 'archetypal' (adjective) + adverbial suffix '-ly'. 'Archetypal' itself comes from Greek elements 'arche-' and 'typos'.

'archetypal' comes from noun 'archetype' (from Greek 'archetypos' via Latin/Neo-Latin 'archetypum'); the adjective 'archetypal' was formed in English from that noun, and the adverb 'archetypically' was formed later by adding '-ly'.

Originally from Greek meaning 'first/primary pattern' or 'original model', the word evolved to mean 'a typical or ideal example'; the adverb now means 'in a typical or representative way'.