A firing head assembly for a well tool includes a shaft, a piston head, a biasing member, and a housing. The shaft has a nose and a terminal end. The shaft also includes a first shoulder and a second shoulder formed between the nose and the terminal end. The piston head slides along the shaft and is positioned between the retaining element and the first shoulder. The biasing member is mounted on the shaft and positioned between the piston head and the second shoulder. The housing has a bore in which the shaft, the piston head, and biasing member are disposed. The housing includes an opening allowing fluid communication between the housing bore and the borehole fluid external to the housing.