1
general::
With great violence or energy; also, to an extreme degree. For example, The cottage was filthy and Ruth began cleaning with a vengeance, or December has turned cold with a vengeance. This expression was first recorded in 1533. Also see WITH A WILL.
American Heritage Idioms
2
general::
Phrase(s): do something with a vengeance
Fig. to do something with vigor; to do something energetically as if one were angry. • Bob is building that fence with a vengeance. • Mary is really weeding her garden with a vengeance., Phrase(s): with a vengeance
Cliché with determination and eagerness. • The angry soldier attacked the enemy with a vengeance. • Bill ate all his dinner and gobbled up his dessert with a vengeance.
McGrawhill's American Idioms And Phrasal Verbs