'arch-killer' is a modern English compound formed from the prefix 'arch-' + the agent noun 'killer'. 'arch-' comes from Greek 'arkhós' meaning 'chief, principal', adopted into English as a prefix meaning 'principal' or 'extreme'. 'killer' is formed from the verb 'kill' + agentive suffix '-er'.

'arch-' ultimately traces to Greek 'arkhós' (chief), which entered English usage via Latin/Old French prefixes and established itself in compounds (e.g., 'archbishop'). 'kill' derives from Old English roots (e.g., Old English 'cwellan' to kill) and developed into Middle English 'killen'/'kilen', leading to Modern English 'kill' and the agent noun 'killer'. The compound 'arch-killer' is a transparent, later formation applying the prefix to 'killer'.

Initially the elements meant 'chief' + 'one who kills'; in modern usage the compound retains the sense 'principal killer' and also allows figurative uses (a chief cause of failure).