This achievement will first require you to visit a "Cosmetic Surgery Clinic" in the game, in order to be wearing bandages. To see where a Clinic is on your map, bring it up by pressing then until you get the "Spots for Avatar" tab. The Clinic icon will be represented by a knife.
Once you've gotten the bandages, they will be removed in around 1 hour real-time, so this is your window to play Multiplayer Challenges.
Once you had had surgery, you cannot re-visit the clinic until the bandages have been removed.
In order to play Multiplayer Challenged, bring up your map again by pressing then until you get to the "Multiplayer Challenges" tab, to which you can pick a race and get going!
Please note: This achievement does not require you to win 20 races, just simply complete them.
To save some time, group this achievement with Multi-Challenger. See the achievement for more details.