Note: Make sure you fart on each one a couple of times, as the trophy has a little trouble registering who you have farted on and who you haven't. So to be on the safe side, do it a couple of times with both the Dragonshout and Cup-A-Smell.
There are four major authority figures in the game, and you need to fart on each of them once for the trophy. These people are as follows:
Minister of Montreal
Principal Victoria can be found in the community center, located next to South Park elementary. The community center unlocks when you start doing quests for the goth kids, you won't be able to go in there straight away. Priest Maxi and Mayor McDaniels can both be found by the Town Hall. Maxi is sitting on a bench outside, and McDaniels is sitting at a desk inside the town hall.
Finally, the Minister of Montreal. He is the only one who is missable! You get one chance to fart on him before he is gone from he game for good. When you are in Canada, you will be taught the Nagasaki fart by Terrance and Phillip. This will then allow you to break the wall found in the dungeons. Break the this wall and fight the dire bears, snakes wolves blocking the minister. Once you have done that, simply fart on him before talking to him. If you talk to him, he'll leave and you wont be able to see him again. If you accidentally talk to him before you fart on him, load Checkpoint save 1 before you move on. This will take you back to the dungeon entrance.