The Subversive achievement has to do with the first heist that Trevor plans after you take control of him. Trevor will plan this with his people (Ron, Wade, etc). This is not the first activity/mission with Trevor but is the first heist. Below will be more details about the mission and its completion. Plus stop reading as to not ruin your experience with this fine game. Also as with every hiest you get to plan how it is executed, my solution deals with the second choice(B).
There will be many little mission leading up to the heist. You will have to steal a cargo helicopter and an exploration submarine. I'm not 100% sure but believe that you will need to own the sandy shores air strip because that is where you will store the helicoper. You will also go to Wades cousin and he will take you to his work, here your going to take photographs of a boat and Merryweather guards. Once these tasks are done you can start the heist.
You will call in Mike and Frank for support. Mike will fly the chopper, Frank will give you support, and Trevor will use the sub. You will most likely want to go to flight school with Mike because it will help rank you up in flying and also get you better at it.
First you will get in the chopper as Mike, and Trevor will get in the sub. Mike will then use the helicopter to lift the sub and go to the designated area. Once there you will drop the sub in the water, and with Trevor use a GPS device to guide you to a package. When you get there just ram the sub into the top of the package to release it and you will automatically grab it. Next head to the surface where Mike will reconnect you and begin flying to the next area. On the way back you will have to fight off some choppers and boats. Once you arrive and drop submarine in the proper area and land the chopper, a cutscene should trigger. After cutscene will be the heist passed/completed prompt and achievement should pop.
If I missed anything or need to change something just let me know. Hope this helps.