He is 'seeking revenge for' his father's murder. [=he wants to harm the person who killed his father]
He swore to 'take (his) revenge on' his enemies. [=to harm his enemies]
The bombing was 'in revenge for' the assassination of their leader.
(..) I want him to know I want him to know. And I want them all to know they'll all soon be as dead as O-Ren. Revenge is never a straight line. It's a forest. And like a forest it's easy to lose your way... ...to get lost... to forget where you came in. That woman deserves her revenge. (..)2003 Kill Bill: Vol. 1