Option 1: No More Secrets.
Your hacktivist group basically has a line into the databases and files of the local Intelligence Agency. They know everything there is to know about every important politician and individual of the nation. Indiscretions, minor and major, crimes, dirty thoughts. All of these things are as an open book.
Even at a simple level, merely the public knowledge that the state has this level of detailed information can cause chaos, especially if the public believe that their country isn't like that, and wouldn't do that.
They can pass on their information about specific people to any interested parties, cause chaos either through blackmail, reputation ruining, or other tactics.
They can sell it to the wrong people, who use it for terror attacks, and then either point to the politicians who didn't stop it, or point to the fact the Agency has this info to imply a false flag operation.
Basically, whatever your nasty heart desires if you have all the dirty laundry of a political elite at your fingertips.
Option 2) Economic and info-economic warfare.
Have them declared dead. Screw their credit ratings up, have them declared bankrupt. Lay data trails to show them being massively in debt, either to banks or criminals. Donate all their money to charities. Falsify compromising messages to their loved ones, or to others faking an affair.
Again, if your hacktivist group is good enough to falsify information on this level, do whatever your nasty heart desires.