to do something with vigor; to do something energetically as if one were angry with it. (Folksy.)
Bob is building that fence with a vengeance.Mary is really weeding her garden with a vengeance.
with a vengeance
Determinedly or passionately, perhaps fueled by anger. After my girlfriend dumped me, I started working out with a vengeance.We're going to have to clean with a vengeance to get the house ready in time.
do something with a ˈvengeance
(informal) do something with great energy or force: After the holidays I need to start working with a vengeance.The rain came down with a vengeance.