The achievement is pretty self-explanatory and isn't too difficult to get. As the achievement says you have to win all the available races in the campaign in order to get it.
*The difficulty you choose to play the game on does indeed affect the ability of the racers. So if you want an easier time getting this achievement, play on easy. Also all the races must be completed before the Authority Bridge part of the game.*
There are a total of 27 races in the game, 16 of which are in Wellspring and the remaining 11 being in Subway Town later on in the game.
There are six types of races you can compete in: Time Trial, Non-Combat, Minigun Race, Rocket Race, Rocket Rally and finally Pulse Rally.
There are three vehicles that you can race with: Buggy, Cuprino, and Monarch.
The Buggy will be awarded to you near the beginning of the game as part of a story-related mission so no need to fret. The Cuprino can only be earned by doing a side-mission for Sheriff Black in which he asks you to get a different set of wheels, this involves receiving a sponsorship from J.K. Stiles in the Mutant Bash TV and finally winning a sponsorship race. The Monarch is obtained by winning it in a race from your racing "rival" once you get to Subway Town and get down to the racing area.
Time Trial - By far the easiest of all the races. As long as you buy the upgraded boost for whichever vehicle you're using you should be just fine. Make sure to effectively use the boosts scattered throughout the racetrack as well.
Non-Combat Race - Pretty easy races as well, simply use the boost whenever you can to get ahead of all the other racers. Buy the upgraded engine and spike performance tires to give you the edge you need.
Minigun Race - A tad bit more difficult than the Non-Combat race. I would recommend simply buying a couple of shields and boosting ahead, using the shields whenever you need to to. No need to go shooting everyone down, they tend to preoccupy themselves if you're a decent distance ahead of them.
Rocket Race - What makes these races more challenging than the Minigun Races is the fact that the rockets when locked on to you will follow and catch up to you and they do a decent amount of damage. For these races, I would recommend upgrading the armor on your car and buying shields and armor restores. For the first lap do not boost ahead or they will all shoot you down. Try firing rockets from the back and using a shield when ever you know you're being targeted. After the first lap you'll be able to safely (to some extent) pull and ahead and boost to the finish line.
Rocket Rally/Pulse Rally - These races can be challenging, especially in the later races. The same rules apply as in the rocket race but because there is no set track, you can be attacked from any side. Make sure your vehicle is fully upgraded because you won't stand a chance if you aren't. It may take a couple of tries simply because you'll need to memorize the positions of the rally points but once memorized you can anticipate where the next one will show up and boost it there. In the later races rally points are taken really fast by other drivers so anticipation is key. Also remember that taking out enemy drivers gives you points as well that count to the over all 50 needed to win the race. (There is only one Pulse Rally race in the game, the only difference is that they have a higher rate of fire and do more damage than rockets.)
**It has been confirmed that the Stanley Express missions are not required in order to get the achievement. Even though the game calls them races you do not need to do them.**