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.
(..) It doesn't matter how careful you are, there will always be weak places in the defense. There is much talk of the revenge of the sons of Ragnar. I know what to expect. And we are fully prepared. I'm not sure you realize the scale of their possible retribution. In the name of our dead father, (..)2017 TvShow: Vikings Title: Revenge Season: 4 Episode 18
(..) We want blood-revenge against 'lla. King Ecbert offered our father up like a sacrifice, so we'll do the same thing to him. We are going to raise an army and avenge the death of our father. (..)2017 TvShow: Vikings Title: Revenge Season: 4 Episode 18