To unlock the Greenist City trophy in Cities: Skylines, you will first need to play the game until you unlock the Big Town milestone which gives you access to Office Zones.
By this point, you will undoubtedly have some industry zones created, once the office zones become available, de-zone the industry areas (yellow) and re-zone them as office zones. Once all of the industry has been removed and the buildings have disappeared, it took around 2-3 minutes playing at 3X speed for the trophy to unlock.
You don't have to worry about any of your service buildings that might be causing pollution such as incinerators, power plants etc. You can keep them running and the trophy will still unlock.