Big Chief is kind of the “final boss” of the game, the last one you have to beat in the list.
After beating Dominator, which had the second place in the list, you’ll be prompted to do the last typical five events before the “challenge night” in which you’ll race against Big Chief.
During the final race you will have to beat Big Chief two consecutive times in order to get the achievement. In fact, if you loose the first time, Dominator will rise again and challenge you for the second place. If you loose the second time instead, you’ll stay second in the list and will have to do other five events before another “challenge night”.
I suggest upgrading your car to at least 4100 points and refine the tuning by yourself, based on your experience, so you won’t get out of the road and get disqualified!