Pretty easy, just a little time consuming (about 30-45 min would be my guess).
From the main menu select new game, enter horse and jockey's names, select horse (doesn't matter which you choose). Then you'll see a menu with 5 different races. "Straight" seems to be the shortest and easiest.
Complete the race. Even if you get a bad start off the line, you should only have to whip 3-4 times. It is straight so there is no need to steer or touch the d-pad or
. Just make sure you finish in the top 3. This will also count towards the achievement "Complete 50 races."
After the race, select main menu. It will take you back to the original menu with the 5 different races, just select "straight" again and repeat.
Do this 50 times and you will unlock this achievement and the "Complete 50 races" achievement.
This can be unlocked using the free trial.