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 also wanted to warn you. You mean, Ecbert sent you. No. I came of my own devising. There is much talk of the revenge of the sons of Ragnar. I wanted you all to be aware of it, and prepared for it. You need not have concerned yourself as to travel so far. (..)2017 TvShow: Vikings Title: The Great Army Season: 4 Episode 17
(..) Say something interesting. You heard what he said, how the little pigs will grunt when they hear how the old boar suffered. So now we're grunting. So what? We want blood-revenge against Aelle? - Yes. - Not only against Aelle. I told you, (..)2017 TvShow: Vikings Title: The Great Army Season: 4 Episode 17