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.
(..) You killed my boy. Maybe you should have raised a man ... ...instead of a some girlie little bitch. God dammit! You came all this way just for your revenge? Well you enjoy it glass. Cause there ain't nothing gonna bring your boy back. Revenge is in god's hands... ...not mine. (..)2015 The Revenant
(..) Killed my son. I lost my family too. Sioux killed my people. I'm going south to find more Pawnee. My heart bleeds ... But revenge is in the creator's hands. You will ride with me ... Your body is rotten. Need to heal. You could die. Yeah! (..)2015 The Revenant