What sort of accident is the Pasuk referring to?
Rashi: It is referring to the woman dying as a result of the blow. 1
What is the meaning of "Nefesh Tachas Nafesh"?
Rashi #1 (citing Sanhedrin, 79a and the Mechilta), Targum Onkelos and Targum Yonasan: It means that he is Chayav Misah 1 (a soul for a soul - for murder).
Rashi #2 (citing Sanhedrin, 79a and the Mechilta): He is Patur from Misah, but is obligated to pay her value 2 (the value of a soul for a soul) to her heirs.
If he is not Chayav Misah, why does the Torah write "Nefesh Tachas Nefesh"?
Perhaps it is to teach us that, since he killed the woman, he really ought to die, only, since he did not aim at the woman, the Torah allows him to redeem his soul by paying.
According to Tana d'Vei Chizkiyah, he is exempt from death and money. How does he explain "Nefesh Tachas Nafesh"?
Moshav Zekenim #1: It refers to Misah bi'Ydei Shamayim.
Moshav Zekenim #2: If he killed the man he intended for, he is killed. Even though this is not a Chidush, the Chidush is from "v'Lo Yihyeh Ason" - Kam Lei bid'Rabah Minei. 1
Da'as Zekenim, Hadar Zekenim: If he intended for the woman and killed her, he is killed. One might have thought that he is exempt, for his primary intent was to kill the other man.
QUESTIONS ON RASHI
Rashi writes that the woman died, and he is killed. How can this be? He was not warned for her!
Moshav Zekenim: He was warned 'do not kill anyone.'