Vengeance is the act of killing, injuring, or harming someone because they have harmed you.
He swore vengeance on everyone involved in the murder.
他发誓要报复每一个参与了这起谋杀的人。
with a vengeance
If you say that something happens with a vengeance, you are emphasizing that it happens to a much greater extent than was expected.
It began to rain again with a vengeance.
天又开始下起了大雨。