GRID 2

The global challenges take place on 5 different locations every week, each consisting of at least 1 event.
The single events of every locations can be of course on different tracks (e.g. for Chicago "The Loop" and "Wabash Run"). Also they can have different game modes like "checkpoint" or "time attack".

By browsing the different locations you will see a leaderboard which displays your current rank across all locations if you participated in at least one event.
This leaderboard consists of all your rivals which also did at least one challenge event of this week (you don't have to compete against the whole community).
You can have a look at your rivals in a separate menu of the online mode.
However, any changes about your rivals have to be done at Codemasters RaceNet webpage and NOT through the in-game menu.
You can access the rivals section in RaceNet here:
https://racenet.codemasters.com/grid2/rivals
From there you can send requests to people from you friend list to make them your rivals, though more rivals are likely to make the task more difficult.
It can also happen that friends who play global challenges will show up on your leaderboard without adding them on RaceNet.
If you have friends on your leaderboard, the RaceNet page is also the place where you must remove them (only removing them from the friend list won't work).
Two rivals will be automatically assigned to you from Codemasters RaceNet community.
Both of them will usually change every week, but while you can't influence the so called "weekly" rival, you can do so for the "custom" rival.
You also have to do this on RaceNet in the "Rivals" section for Grid 2. Select the "custom" rival and then choose the "edit" option. Then you will be presented with some drop-down-menus where you can select the attributes you want your new rival to have e.g. "less XP than me".
You have to be aware that this changes will take effect for the next global challenge week and won't drop a current annoying rival immediately from your leaderboard.
The other spots are for friends and can be controlled entirely by you.

Unfortunately it can become a bit of luck based now, if you have rivals who will actually compete against you or not.
You can't influence that, so it makes sense to regularly check the state of the leaderboard before the current week's challenges expire.
By doing more events you can increase your points, but if no one competes against you a single event can already be sufficient to get this achievement.
You also need to be aware that your total score will be lowered when rivals beat your score (even if they remain lower ranked than yourself, this can still help other competitors to beat you).

For every event you did on a challenge you will receive points depending on how well you did.
Scoring a first place among your rivals (this includes friends that are set up as rivals) on this event will net you 2000 points.
For every position below 1st place you will get your score lowered by 200 points, e.g. 1600 points for a third place.
This points will sum up over all events of the challenge and are your score for the leaderboard.
So you don't necessarily have to win every event, as long as you're number one of the leaderboard when the challenge expires (the remaining time is displayed somewhere close to the top of the screen).

The achievement will pop when you access the global challenges menu in multiplayer mode again after the challenge has timed out with you in first place.
As a nice additional reward you will also get 30k in credits for your victory, which you can invest in new cars and upgrades.

Personally I received mine today and all challenges have been reset for another week, which implies that they time out at 12'o clock (mid day in Central European Time I think, since I'm in Berlin timezone). Though this could be subject to change in the future.

Additional Credits:
(Please also have a look at the comments section to view the full posts of this contributors if you are interested in more details)

Thank you and credit goes to BipeFlyer for making me aware of the rivals issue and some other incorrect details in the previous version of my solution.

Another credit goes to ScuzzyBunny for clarifying on the rivals issue (also see comments section).

Credit goes to KnucklesNorwood for pointing out that you actually can influence one of your automatically assigned rivals and for your useful insight in the rivals issue in general.

Also I wish to give credit to Nekro Neko for correcting me with the locations (instead of challenges) and very useful insight in the points system, which determines your score.

Thank you to B A R 4 D for adding the amount of in-game credits you will receive along with this achievement.

So I expected this to be difficult and tedious.
In fact, you can do this by yourself and without any stress.
You will most likely have to make an RaceNet account which shouldn't take longer than 5 minutes.
After that, go to Online, Events, than Global Challenge. Search for a race you like, start and end the race regardless the outcome. Wait for 1 week, check the stats after 1 week and if none of your friends/rivals happened to play this game or even beat you, the achievement will pop.
Afterwards you will also have enough money to upgrade your car for another achievement.