I would start with the city of New Haven, CT that started issuing ID cards this week to illegal aliens to use for city services and local businesses.
Cities and government agencies have deep pockets but that also means they will fight tooth and nail and would draw out a lawsuit well beyond the resources of a private citizen to pursue.
My tactic is to go after the SMALL businesses that might actually be afraid of the lawsuit and be willing to settle — and swear off hiring illegals. That would dry up the jobs and without jobs most illegals will go home.
It may seem underhanded and mean to go after the Mom & Pop businesses, but small businesses are the largest employer in the US when taken as a group. That is where the message needs to hit home that hiring illegals is not going to profitable in the end.