A distressed fighter pilot witnesses a princesses urgent hologramic plea, his family now dead, he must seek a Jedi master to learn from, saving the princesses planet from destruction.

You have included most of the essential story elements but at the beginning of the story, Luke is really not a fighter pilot yet. He’s a farm boy who doesn’t believe he could ever be a jedi fighter. Can you include this in a concise way at the end of the logline?

“he must seek a Jedi master to learn from” sounds like it is the story’s main goal, which it is not. You may easily leave this bit out. It seems more important to retrieve the plans, save the princess and destroy the Death Star.