Antagonist's Motive

Question: In my plot the antagonist is seeking revenge while the protagonist's main motive is to stay alive. Is there anything specific I need to add to the plot since the antagonist has the motivation that moves the story along?

Answer: A protagonist usually has two essential functions. He pursues the story goal and he considers the importance of the story goal.

In some stories however, it is the antagonist who pursues the story goal while the protagonist tries to prevent the goal from being achieved. It sounds like you're writing this type of story.

But even in this type of story, the protagonist still must consider the importance of (in this case) preventing the story goal. Obviously, he wants to stay alive. But the story may be stronger if he has other considerations, other reasons for wanting to stay alive, that concern the big picture. Will the world of the story, the lives of the other characters, be worse if the villain succeeds? Can you make the protagonist want to survive for the good of others, not just himself?

For example, consider the story of Les Miserables. In that story, the protagonist is an ex-con who broke parole and is being pursued by a policeman who wants to throw him back in jail. The reader has a certain sympathy for the ex-con, since he was falsely convicted in the first place. But that sympathy leaps to a whole new level when he adopts a penniless orphan girl. From them on, his staying out of jail is necessary to give the girl a chance at life. Earlier, the ex-con also risks being caught to stop another innocent man from going to jail.

Considering that he is the only person who can help these people, gives the ex-con a much stronger and more sympathetic motive for thwarting the policeman's aim.

The advantage to these considerations is that they show how the protagonist is a better person than the villain. After all, if the villain is after revenge, presumably he feels he has been wronged. You don't want the reader sympathizing with the villain, so make the protagonist someone who deserves to live.

Of course, all this assumes you're writing a story with a happy ending. If you're writing a tragedy, along the lines of Oedipus Rex, then the protagonist will more likely consider his errors and the agony they have brought him. The reader will then be sympathetic towards his plight, but still see that his death is necessary for the greater good.