You can also link this achievement with
Basically after completing the quest 'Old Times' the hippodrome should unlock go up to the doors (or fast travel to it from the map) to gain entrance.
Simply select the Nike's Winged Victory tournament and go through all three races. You do not have to win all three but the nearer to the top you get the better your chances for victory! After winning the tournament overall the achievement should unlock!
Let's keep on cheevin' together!