SEO to push down - content and raise + content

Hello! My client has some negative press online that contains their personal name. They have a documentary about their side of the story on Youtube, as well as a successful business. We need to get more positive sites ranking higher than the negative. I have some SEO experience but not any time! I have ideas of what should be done! Is this what you do and in what ways would you go about it? Also please explain how long you think each task involved in the project would be. It may be that we hire a few people for different tasks depending on specialty.