'arch' (from which 'archest' derives) ultimately originates from Ancient Greek, specifically the word 'arkhós' (ἀρχός) meaning 'leader' or 'chief', transmitted into English via Latin and Old French forms of the prefix 'arch-' and the adjective 'arch'.

'arch' passed into English through Latin/Old French usage of the element 'arch-' and Middle English 'arch(e)'; the adjective meaning 'mischievous' developed later in English, and the superlative form 'archest' is an English formation using the -est suffix.

Initially associated with leadership or chief status ('leader, principal'), the sense broadened in English to include a figurative 'chief' intensity and a separate colloquial sense of 'mischievous' or 'archly playful'; 'archest' therefore came to mean 'most chief' (rare) or 'most mischievous' (attested in literary/dated use).