This trophy will take 6 hours of game time to unlock.
At the beginning of the game, you should go south from the Ranger Citadel to a place called the Ag Center. Within here there are big plants (pods) that are purple. When you walk near them they will explode. If you have any characters too close, then they will get infected.
The infection starts with a 4 hour countdown. When this reaches 0 then the infection gets worse and a 2 hours countdown starts, your character will then start taking damage periodically. If they run out of health then they fall unconscious and then wake back up with 1 health, this will repeat unless you heal them so they have more health. Leaving them with low health will not harm this trophy. When this reaches 0 your character will turn in to a pod person and you will get the trophy.
There is a bug for this, in that if you get infected by another pod then the timer resets to 4 hours again. This is very annoying if you are continuing playing whilst counting down the timer. My solution for that was to have more than 1 infected player, and always try to burst the pods with 1 of them so that the others do not reset. If you are within the 2 hour countdown, then getting infected by another pod will start the 4 hour infection, but also leave the 2 hour one.
You can not change the system clock to get this faster. So you have to wait for the 6 hours. There is a cure for the infection, so you could get infected, obtain the cure and play until the 2 hours to go mark and then wait it out, reload a save once you get the trophy to cure them and carry on playing. Alternatively, you could keep one save with the infection and load it when you are not playing to countdown the time whilst you do other things.