The "how" here is pretty simple: either collect 42,000 signatures and recall her, or run a serious candidate (someone with governing experience, not a professional activist) against her when she comes up for re-election.

"Demanding" that she resign is not going to do anything, she clearly has no shame.

Complaining to Fulop and Murphy is not going to do anything, they have zero incentive to take on a brutal fight against HCDO.

There is not a shortcut here, if you want to get rid of DeGise you have to beat her.