。
She hit me on the head with a hammer.
Literal
She [topic-は] hammer [with-で] my head [object-を] struck.
で here marks the hammer as the means or instrument of the action — the same で that introduces transportation (バスで行く), language (日本語で話す), and material (木で作る). 殴る ('to strike, hit, punch') is a forceful verb specific to physical violence between people, distinct from 叩く ('to hit, tap') which is gentler and more general. Note that Japanese says 私の頭を — 'my head' as the object — rather than 私を ('me') with the body part separately; this is the 'whole-and-part' construction common in Japanese and many other languages.