This can only be unlocked if you've done the Palisade Bank heist (M12) instead of saving the bomb-maker (M11).
Once you're in the vault that the mission requires you to reach, there will be a safe in it. Access it however you want and get the Antidote that's inside.
That item is pretty much useless up until you find Miller in the catering area during M16/M17. After the initial conversation/cutscene, you'll be asked whether to stop Marchenko or save the delegates. After your choise, talk to Miller again and when asked, choose to give him the antidote. You'll save Miller and unlock the achievement.
Note: Regardless of what others say, giving Miller the antidote won't void "Spokes in two wheels", since you reach the delegates and prevent them from drinking any champagne in the first place. Therefore, both achievements can be unlocked in the same playthrough and without any reloading.