From Old French 'achever' (to bring to a head), where 'chief' is Latin 'caput' (head), not 'capere' (to take).
To successfully reach a goal or accomplish something through effort or skill.
From Old French 'achever' (to bring to a head, to finish, to complete), from the phrase 'à chief venir' (to come to a head), where 'chief' derives from Latin 'caput' (head), from PIE *kaput- (head). Despite its '-ieve' ending resembling the '-ceive' words from Latin 'capere' (to take), 'achieve' comes from a different Latin root entirely — 'caput' (head), not 'capere' (to take). The original metaphor is vivid: to achieve something is to bring it to a head, as one brings a boil to a head or drives an arrow to its mark
Though 'achieve' looks like it belongs to the 'receive/perceive/conceive' family (all ending in '-ieve'/'-eive'), it has a completely different etymology. The '-ceive' words come from Latin 'capere' (to take), while 'achieve' comes from Latin 'caput' (head) — a classic case of superficial resemblance masking unrelated origins.