If you're as frustrated with the other guides as I was hopefully this'll help.
From the main menu select Franchise Mode and then create new league.
Select Active Roster from the upper cloud menu and choose whichever team you like.
Then under more options select Starting Point -> Fantasy Draft then back up to Start Playing.
Start fantasy draft and then when making your selection use RT to switch to QB and then press Y to filter by last name.
Then scroll down to Joe Burrow or Justin Herbert depending on your active roster, select whichever one is available, make your pick and the achievement should pop.