From Latin 'ad-' + 'complere' (to fill up) — accomplishing something is literally filling a task to the brim.
To achieve or complete successfully; to bring about or carry through.
From Old French 'acompliss-' (stem of 'acomplir,' to fulfill, to complete), from Vulgar Latin *accomplēre, from Latin 'ad-' (to) + 'complēre' (to fill up, to complete), from 'com-' (together, intensifier) + 'plēre' (to fill), from PIE *pleh₁- (to fill). The underlying image is of filling something up to completion — a task conceived as a vessel that overflows when fully done. The root *pleh₁- is enormously productive: it gave Latin 'plēnus' (full), English 'full' through Proto-Germanic *fullaz, 'plenty,' 'plenary,' 'replenish,' 'supply' (sub + plēre), and even 'folk' and 'people' (from *pleh₁- via the sense of a 'fullness' of persons