The Jovian Concord update has trivialized this achievement. With the update, you can now view which 5 races are active on a given day by simply mounting your K-Drive and opening up the full map of the Orb Vallis (hold the button). There will be 5 purple icons scattered across the map. Simply visit these 5 locations every day after reset (8:00 p.m EST during the summer) and do the races until you eventually get all 22 done. This will also help you reach max rank with the Ventkids quickly, as well as level up your K-Drives for that sweet MR.
Be sure to tell others about this change, as it was undocumented in the patch notes, and the only place I could find this information was on the wiki, and from a comment on the formerly updated map the community made, linked in the other solutions.
For more information on the races check out the wiki page here: https://warframe.fandom.com/wiki/K-Drive_Race
Edit: The races only appear on the map after you have constructed a K-Drive using parts purchased with Ventkids standing. The initial, stolen K-Drive will not cause the races to appear (Credit: OLOT).
Edit 2: Apparently the races can now be viewed on the map while riding the default free board (Credit: UltimateHero128).
The wiki seems to confirm this:
Fixed K-Drive races not appearing properly on the minimap when using the default K-Drive from the Vox Solaris Quest."