The sponsorship challenges consist of a number of ranks tied directly to performing an individual trick, the same tricks that increase your popularity. The different ranks define the number of times the trick must be performed in order to complete each challenge.
Despite the achievement description, each rank counts a 1 challenge, e.g. reaching rank 4 of the drifting sponsorship challenge will count as 4 challenges completed. You can check your status any time in the 'My Profile' menu.
Most of these will unlock naturally as you progress through the game and raise your popularity, so you will complete 20 in no time. Also be aware that any tricks you do in multiplayer also count towards this achievement.