Just disconnect everything.
Just Cause 3 does this silly little thing where it demands you log in to its servers just so you can get access to its leaderboards. The problem is, you lose your connection to the servers every few minutes anyway, so why bother?
Unfortunately, there isn’t a way to disable the online stuff from within the game so far, but we have found a temporary workaround for it. All you have to do is go to the settings menu on your PS4, and uncheck the box that connects you to the internet. This will stop the game from attempting to log back into the servers each time you enter the pause menu or bring up your map.
It isn’t an ideal solution, but unfortunately it’s the best thing you can do at least until a patch is released.