The old woman across the way is whipping the boy again (1-2)
The key word in these lines is "again." The woman is a clearly a, ahem, repeat offender. In addition, "again" is a word that describes something that has happened before, and by the end of this poem we learn that this woman has a long history with violence.
and shouting to the neighborhood her goodness and his wrongs. (3-4)
While it seems at first that the woman is merely punishing the boy for who-knows-what (stealing cookies again?), the fact that she is obsessed with telling the whole world about her "goodness" makes us think there might be a deeper motive for her violence.
She strikes and strikes the shrilly circling boy till the stick breaks in her hand. (9-11)
These lines are really violent. Not only does the stick break, and the woman "strikes and strikes." The sounds of violence are everywhere. That S sound in "strikes" pops up several times—"strikes," "shrilly," "stick."
My head gripped in bony vise of knees, the writhing struggle to wrench free, the blows, the fear worse than blows that hateful (13-16)
This is hands-down the most vivid depiction of violence in the entire poem. "Gripped," "vise," "writhing struggle," "blows," and "blows"—it's as if the rhetoric is laid on pretty thick to make sure we get the message that this is a very, very traumatic memory.
Words could bring, the face that I no longer knew or loved (17-18)
Violence makes monsters out of people we thought we knew, and people we used to love. That is what is happens here, and this may be why the relationship between the woman and the boy isn't described in any detail. Violence destroys relationships.
avenged in part for lifelong hidings she has had to bear. (23-24)
"The Whipping" is a poem about violence and about violence as a way of getting revenge. And strangely, it seems to work. The woman is mad about things she's hidden, or about having to hide them, so she beats the boy really bad and is "avenged in part." Okay, hold on—is she actually avenged, or does she just think she is? Hmm.