GTA Online's collaboration with Dr Dre is still going on and the Producer award is closely connected to the artist, although it's somewhat vague about the details.
GTA Online players can get the Producer award if they spend enough time watching Dr Dre working in Record A Studios, the same place where you had to wade through a pile of gunmen sent by Johnny Guns. However, people found themselves confused as the only time they actually saw Dr Dre in that place was during the same mission and its ending.
The trick is that you will need to complete The Contract storyline, including Dr Dre VIP contract and possibly the three Short Trip missions since the first one in the chain offers a tour of the studio.
From that point on, Dr Dre should be making regular appearances in the studio, at which point you can go and see him at work. However, you can't just go at any time since Dre's schedule pretty much dictates he is at work every other day. So if he works Monday, Wednesday, Friday and Sunday one week, he will work on Tuesday, Thursday and Saturday the next.
If you're not sure whether you nailed Dre's rhythm down, you can check a real-time countdown to Dr Dre's visits , which will show when he will pop up next, in your local time.
Once you're there, you will just have to hang around until the achievement progress fills up, at which point you will finally get the Producer award.