To get this trophy, you have to keep your speed above 20mph for the entire duration of Lombard Street. In case you are not aware, this is the winding street in San Francisco with 8 hairpins, one after the other - making keeping your speed up very tricky.
This is the street that you need to go down on the Driver: San Francisco map:
Head for the street, picking a car that you are happy to do repeated handbrake turns in I.e. A Nissan 370z, as just one example.
There are bollards on each corner, to make you life more difficult (but not as difficult as if there were flowerbeds all the way, as in real life!). Go down the street first, to clear out the bollards - this will allow you to cut the corners and keep your speed up.
With this done, return to the top (you need to take the street from top to bottom) and begin. Use your handbrake to drift over each corner, keeping the turns tight into the corner so that your speed is maintained.
Once you pass the bottom, as long as you were always over 20mph throughout the length of this famous street, you will unlock the trophy. See the video below if you need some more tips: