'archrascal' is formed from the prefix 'arch-' (from Greek 'arkhos' via Latin/Old French 'archi-' meaning 'chief, principal') combined with 'rascal' (from Old French 'rascaille' meaning 'rabble, low people').

'arch-' (from Greek 'arkhos') was used in English formations (e.g. 'arch-enemy'), and 'rascal' came into Middle English via Old French 'rascaille'; the compound 'archrascal' (sometimes written 'arch-rascal') arose in Early Modern to modern English as an intensifying compound meaning 'chief rascal'.

Initially it conveyed the sense 'chief of rascals' or 'principal scoundrel'; over time it has been used more broadly as an emphatic term for an especially bad or mischievous person, a meaning that persists.