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The following are the requirements for Gold Race badges (all must be collected for the achievement):

Boom! - Achieve a speed of over 250 km/h:

There are a couple of good ways to get this. On the Serenity tricky event in the Himalayas, there are a few long rails where you can boost up to this speed. Make sure to get yourself into Tricky mode, and just boost like crazy once you get to the rail. Alternatively, equip a wingsuit and pick a track with good jumps (the wingsuit required runs are good places for this). Get a good jump with a lot of air, and deploy your wingsuit, then just nose dive as far as you can. You should get this on the way down. Naturally either of these is easier with a higher level character equipped with higher level gear.

Lead Foot - Maintain 100 km/h for 40 seconds:

See "To the Metal" just below.

To the Metal - Maintain 130 km/h for 40 seconds:

This can be done on Serenity as well, or just any location with long rail slides. Again, get yourself into Tricky mode, and boost like crazy on a rail. Once you get to the end of the rail, rewind to the beginning of the rail (making sure that you're still listed above 130 km/h, you'll still see this listed during the rewind) and then go the length of the rail at full boost, then rewind again to the beginning, boost the length of the rail, etc. Just keep rewinding till you get it. Note, you will decrease speed with each successive rewind, so it's best to get going above 200 km/h or so so you won't risk going below the 130.

How Do I Not Boost? - Boost for more than 2 hours total:

This is cumulative, and should come with time. If you're going for other badges/achievements, you won't have to work for this. If you need to however, simply load up a race or trick event on one of the peaks in Alaska or the Rockies (any location that's "safe" will work...make sure there are no ledges or holes to accidentally jump/fall into), get yourself into Tricky mode, and boost like crazy while holding B to manually tail slide (tail sliding will keep your Tricky meter engaged with unlimited boost) down the mountain while keeping on the boost.

Cross-Country - Ride a total of 200 Kms in Race Events:

Again, this is cumulative, and should come with time while going for other badges, especially if you're going for the Global Event badges which require you to participate in 50 race events. It should come naturally while playing through the game, however if you're wanting to boost it, I would suggest going into Global Events, pick any range/mountain, and create a custom race event, and just complete the race. This way you're also working towards the "Compete in 50 Race Events" and "Compete in 50 Custom Events" badges at the same time.

If like me you struggled to find a place to go over 130km/h for 40s then use this guide
-Go To Alaska or Serenity in the Himalayas
-Find a suitably Long Rail
-Make sure you are going over 130 km/h while on the rail
-Simply ride the rail to near the end then rewind to the start and repeat until the badge pops up!

Of you need help on another badge in the race category Im happy to add it to this solution!

Good Luck!

If you are struggling with the 130 mph for 40 seconds like I was than you can go Himalayas - Mount Everest - Burnout on any mode. Watch the video to see where to go and what to do. You can still use a wing suit but it is not necessary to get this. After 40 seconds it will pop. Let me know if you need help or clarification. This will also help you work on the This Gear is Golden Achievement. Good luck!

If you are working on the 2 hour boost challange there is a very easy way to do this. Go to a race in siberia (i think the shortest one worked for me perfectly). Go down until you are shortly before the finish line. In this map there is a large open space there. Now u need to go into tricky mode, before you reach that point. Turn around and boost your way back up the hill until you get negative points for "no flow". This counts as a trick and as long as you dont drive down too much it will always be there and your tricky mode wont stop. As soon as you get that just drive a big infinite symbol (how ironic) into the snow and keep an eye on your "no flow" points. When you "lose" those points just drive back up again until u get it and repeat the hole thing. Now you have infinite boost. Have fun! :D