There are two steps to this achievement:
1) Unlock all Operators
2) Play a round with each Operator
The difficult part is unlocking all of the Operators, which is going to cost you a lot of Renown. Step One for this achievement is the same as earning the Full Roster achievement. I have made a separate guide for Full Roster, but I'll just paste the solution below.
"There are two attackers and two defenders within each CTU, for a total of four Operators. With the five CTUs, that means you have 20 Operators to unlock. The Renown required to unlock Operators increases each time you unlock an Operator in a CTU, (the first costs 500, the second is 1000, then 1500 and finally 2000). It costs 5000 Renown to unlock all Operators within any given CTU, so you are looking at 25000 total required Renown to unlock every Operator.
Fellow TA user X1 Two helped to figure out the fastest way to earn all of the Renown you will need to unlock all of the Operators. Playing the single player Situations mode in its entirety and earning three stars on every mission will earn you somewhere around 7000 Renown (this also earns you the 50G Completionist achievement). Viewing all of the tutorials from the main menu will earn you an additional 800 Renown. However, replaying the Situations after your first playthrough yields very little Renown per hour, so this is not a good method to farm Renown. For the remaining ~18000 Renown, X1 Two says that playing Terrorist Hunt Elimination missions on Normal difficulty is the fastest way to consistently earn Renown. If you are consistently winning and surviving during these missions you can earn about 1700 Renown per hour. So it will take a little more than 10 hours of Terrorist Hunt missions to earn enough Renown for this achievement. This will also help you get some of the achievements that you need to play a lot of Terrorist Hunt for, so it seems to be a pretty effective use of in game time. I will update this if any better strategies are discovered."
After you have unlocked all Operators and earned your 50G Full Roster achievement, you need to play a round with each operator. In a regular multiplayer match, just switch Operators after you complete each round. You can get through 3-5 Operators per game this way, and there are only 20 in the game so far. It shouldn't take you too long to get this after you have done all the hard work earning Renown. Hope this helps!