From Longman Dictionary of Contemporary Englishwoman/man with a missionwoman/man with a missionsomeone who is very determined to achieve what they are trying to do – often used humorously → mission
Examples from the Corpus
woman/man with a mission• Powered by a man with a mission.• A man with a mission who suddenly loses his faith.• How can a 77-year-old man with a mission admit that he was wrong all along? 