'archhypocrisy' is a Modern English formation combining the prefix 'arch-' and the noun 'hypocrisy'. The prefix 'arch-' ultimately comes from Greek 'arkhós' meaning 'chief, principal', while 'hypocrisy' comes from Greek 'hypokrisis' meaning 'acting, pretense'.

'arch-' entered English via Latin/Old French as a prefix meaning 'principal' or 'extreme', and 'hypocrisy' entered English from Old French 'hypocrisie' and Latin 'hypocrisis', originally from Greek 'hypokrisis'. The compound 'arch-' + 'hypocrisy' is a later Modern English coinage formed by productive prefixation to intensify meaning.

Initially the components meant 'chief' (arch-) and 'acting/pretending' (hypokrisis); combined in Modern English they evolved into the intensified sense 'the chief/most extreme form of hypocrisy', i.e., 'extreme insincerity or pretense'.