EDIT: According to AceMcCloud's links below, this achievement is now unattainable due to Autolog being taken down for this game. EA does not have intent to restore functionality.
This is for a stage in The Run, all races in that stage included.
Becoming the leader refers to your personal friends list for that particular stage.
If you don't have any friends who have completed a stage, you cannot get the achievement. Creating and playing on a dummy account (as Reaper posted) is one way to fix that issue.
If you have many friends who have played the game and they're plenty better than you, either practice a lot or delete the ones above you on a stage where there is a least one player below you. I did not try the delete method - I just went and beat my friend - so I can't confirm that method works, but I don't see why it wouldn't.
If you're trying to earn it legitimately, you can go back to earlier stages with cars you've unlocked later in the campaign. This can give you an edge if friends did not also do so and their current time is with a 'lesser' car.
If you try this on a stage with gas stations, memorize the tracks and try to match the car to the road. Most players playing through the campaign aren't going to be using gas stations in strategic ways.