Indexing bird radical on the right (simplified from 鳥). Declares 鸭 a kind of bird. Same family as 鸡 (chicken), 鹅 (goose), 鸽 (pigeon), 鹰 (eagle). The bird radical is what makes 鸭 unambiguously duck rather than an unrelated jiǎ-syllable.
Left 甲 supplies the sound (jiǎ → yā — palatal drop in Mandarin; both share the same Old Chinese velar onset cluster). 甲 itself depicts a turtle plastron or armour; here purely phonetic. Same phonetic in 押 (yā, pledge), 闸 (zhá, sluice gate).
