This achievement is currently unobtainable.
The way this achievement is supposed to work is that the game auto assigns your gym a new rival after a set amount of time, about 2 weeks. Then that gym would be your rival for a few days, allowing you to get the achievement before the countdown starts again. The problem now is that the countdown for the next rival assignment is over 6000 days. That's 16 years!
So until EA fixes the timer, all three Represent the Crew achievements are unobtainable. As far as I can tell it's been broken since early January 2013 so they're not exactly in a hurry to fix this. You can try bugging EA about it, but don't get your hopes up.
Will update this solution if this is ever fixed.
UPDATE: Dec. 30 2013
Don't get excited, these achievements are still broken. I decided to check in since the game has been on sale for $5 this week.
This is what the gym rival screen currently looks like.
I took this 2 days ago, Dec. 28. The clock showed a new rival assignment in 5847 days. Using http://www.timeanddate.com/date/dateadd.html
that works out to Dec 31 2029.
Enjoy the 16 year long wait for this achievement, courtesy of EA!
UPDATE 2: May 24 2018
It has been 5 years since these achievements were broken and the game has now gone backwards compatible a few days ago. Are they fixed? NOPE!
4,239 more days to go.