This one is done in your My Team mode, simply by just progressing.
Secondary Sponsers are the ones you choose when you reach Team Acclaim levels 2 and 5, by just doing practices and racing and obtaining Resource Points.
To choose your secondary sponsers:
--> My Team mode home page (as long as you have not gone to a Race Weekend, otherwuse you'd have to complere that first)
to the "Corportate" tab
--> In the first Sponsership Tab, select the "+" on Secondary Sponsers (once you reach the Acclaim Levels"
--> Look at the Goals of each Sponser and choose the one you know you will achieve (if you don't care about the cash bonus', or simply choose one that has a good weekly, great bonus, and do-able goals)
i personally chose Z-A-I-N-E-T-T-O, which has the goal of answering at least 2 interview questions during the whole weekend (after practice, after qualifying, and of course after the race), and SEREN, which has being in first for at least 2 laps.
--> Once you've chosen the two Secondary Sponsers, go to your next Race Weekend
--> Complete the goals required for both of them (so for me, hold 1st for 2 laps and answer questions)
--> At the end of the race and after clicking "Advance", if you wait, you will see that you recieved two cash bonus' if successful in completing the required goals
The achievement will be yours once you finish the Race Weekend