This is not my info. I pulled this info from comments over at Brokers Don't Care How You Win (thanks TheBigDeeb and Elodeon). I am posting this info here to help others, who are looking to complete this for the Brokers Don't Care How You Win achievement.
This quest can be completed in the Untethered Space. For those who don't have some form of travel form or just really want to blow this achievement out of the water, this can be done easily by geting yourself some [item=242371]. These need to be looted in the Untethered Space, which have been known to show up at the following locations:
/way 49.67 17.05 Untethered Xy'bucha
/way 49.65 26.65 Untethered Xy'bucha
/way 50.74 58.45 Untethered Xy'bucha
/way 53.75 45.37 Untethered Xy'bucha
/way 54.81 48.18 Untethered Xy'bucha
/way 61.33 39.11 Untethered Xy'bucha
/way 80.35 48.69 Untethered Xy'bucha
Once you have one, go back to the eco-dome and pick up the quest. Head on over to where you need to start the quest. Before you start the race, drink your Untethered Xy'bucha. Once done, start the challenging version of the race and then you can do 1 of two things:
1. Run through all the arrows to the end
2. Run straight to the end, ignoring the arrows. The end can be found here: /way #2371 74.36, 27.51
ALTERNATE STRAT
It should be noted that the Untethered Xy'bucha is NOT needed to get this achievement. You CAN just run to the end without it, picking up speed boosts as you see fit. Either strategy works. Pick one and have fun!