The Final Route appears after you beat every other race in World Xplorer and is a really hard challenge. i had to restart the first track over 100 times (it's probably the hardest race)... but in the end every race is doable, trust me. (with a bit patience and skill)
whats the trick?
ultimate charge is the key... after your used nitro runs out, refill it with a drift and try to block others racers behind you after you overtake them. if you block your enemy successfully, you have a good chance to earn more nitro to defend the first position.
for Final Race 1 - 4 i choose the Angelus... for Final Race 5 the Ultranova.
Ultranova has the ability to refill the nitro through the ultimate charge reaaally quickly. if you can master this drift method with this car, you have nearly endless nitro and the enemys are not longer a problem (and you can win every race of the final route)... but this car refill his nitro with normal drifts really slowly, so if you mess up an ultimate charge drift, you maybe have to restart the entire race.
be sure to use a car that you won online (Kilik Angelus or Cybersled Ultranova as example) on final route 4 to unlock another message from Reiko for this achievement:
i know this solution makes this route not easier, but maybe it helps a bit and give you new hope to beat it!... the youtube video (thx to the uploader!) shows you the perfect moment/method to refill your nitro with the Ultranova, but if you have mayor trouble with this car, you can also use the Angelus - like me, but in that case you have to drive aggressive, block your enemy and you need some luck. ;)