For this achievement you must select a character in character select at least 300 times over arcade, versus and online mode. While doing all your online matches keep that in mind and stick to the same characters if possible to assure you get this.
If you decide to turbo boost as mentioned under The Endless Road the game will automatically reselect your previously selected characters so it will gradually add to your count when you leave it on overnight.
To check your progress for this achievement, go to Player Data at the main menu. Select Player Records. Hit twice to see your most used character to keep track of this achievement.