The best way to achieve this is to obtain a fast vehicle and just speed down a major road with a long straightaway. Most of the Hidden vehicles work very well for this, though it can be accomplished with a number of the regular vehicles. Try to avoid hitting other cars or obstacles (street lights, signs, mailboxes, trashcans, etc.), as this will only slow you down.
Try driving the long streets, such as Hollywood, Sunset Blvd, or Van Ness at night or on a rainy day, when there is less traffic.
Note that you must drive on a road for the achievement to register, driving along the bank of the Los Angeles River, for instance, will not work.