How should I search for a person or service to remove derogatory information about myself?
There are some offices that can handle this but you have to pay alot of USD dollars
When you requested removal of content from Google you use the public removal tool located at
Services to remove your name from search engines
Remove your name
Reputation Management firm
I agree with both of the above
One last try would be to contact the web host about the abuse and personal attack. There are Service Providers with standards who won't tolerate personal attacks and will ask the site owner to remove it duo to your complaint.
In general it depends on the kind of attack. If someone disagrees with your methods, political attitude and stuff like that you cannot prevent them from expressing their thoughts and saying "don't listen to him, he's BS" .
The only possibility is to ask the owner of the site in question to voluntarily remove the information about you. But then it may take some time for the search engines to come visiting and update their results. Google is normally quite fast though.
If the owner of the site refuses to remove the information about you, then as James says, there's nothing you can do about it. The best strategy in this situation is to ensure that there is lots of positive information about you out there online to counteract what negative things might be getting said. So build up a web presence - website / blog, Twitter page, Facebook page....then when someone searches for you, hopefully your stuff will be at the top of the page and the negative stuff will be pushed to the bottom.
Have you ever heard of freedom of speech? Just because someone says something wrong or 'derogatory' about you doesn't automatically give you a right to remove it. Sorry, that's just not how the world works.
I'm sure someone else will chime on this thread saying you could litigate, but you should only consider that if you're American and the site in question is hosted in America, and you can actually prove that what they said is either wrong or financially damaging. Otherwise, forget it, and move on.