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.
(..) and then you can tell everyone that this was all just a big mistake. Huh? Right? Buddy? I just want you to know that even though you tried to terminate me, revenge is not an idea we promote on my planet. -Oh. Well, that's good. -But we're not on my planet, are we? No. Okay, come on! (..)1995 Toy Story