、。
She complains of headaches — and frequently at that.
Literal
She [topic-は] headache [object-を] complains-of, that-too frequently is.
The sentence breaks into two parts: the main statement 頭痛を訴える, and the emphatic afterthought それもしょっちゅうだ ('and frequently at that'). それも adds a second, escalating detail — it's not just that she complains, it's that she does so constantly. しょっちゅう is a colloquial adverb meaning 'all the time / constantly,' more casual than 頻繁に or いつも. 訴える ('to complain of / to report symptoms') is the standard verb for reporting physical complaints.