Through earning your Influence Points you will be prompted by Sponsors to complete for their brands. You need to try out for their challenges through the Media and Sponsorship section of the Mountain Map. Once the Sponsor prompt screen pops up you either have a choice to accept or reject .
If you do not have the option to Stay Loyal then accept the offer. At some point while Sponsors are offering you their brand the rejection option will just into the Stay Loyal option instead. Staying Loyal will earn you 20 Influence points and this achievement.