This opened for me in the second season of career, after winning every tournament up to this one.
To win you have to do the following:
Round 1: Win 6 legs
Round 2: Win 8 legs
Quarter Finals: Win 10 legs
Semi Finals: Win 11 legs
Final: Win 13 legs
I found the best and quickest way to do it was:
T19, T19, T19
T20, T20, T20
Bull, Bull, Bull
You have to do the whole tournament without leaving the career mode or turning your xbox off as this disables the achievement.