Before you can unlock this you will need $200,000 with Franklin
Once far enough into the game after you have stolen the Lost's plane as Trevor the option to purchase the Cab Co will be available to you, now select Franklin as your active character and travel to the upper right hand corner of Los Santos City in 'East Vinewood' where there will be a House icon with ($) inside it in this location.
Travel there and buy the Downtown Cab Co. for $200,000 by walking up to the For Sale sign and press
twice, once the purchase is complete you will immediately get a call from Raul who introduces himself.
Now you need to wait for a second call from Raul which may take some time so try to stick with Franklin and just play missions like normal, after 1-3 real hours you should get the phone call. xxxDarkRuleRxxx notes that you can speed up the phone call by sleeping 6+ times in Fraklin's safehouse.
In the call Raul asks if you'd like to work on a 'Private Fare' to earn some extra money. Push the
to Accept. After this, you have on your Map a new green Symbol 'P'. Drive to them and pickup the Passenger.
Play the mission out and the achievement is yours.