The Apocalypse Challenge is a difficult, multi-generational challenge that begins with restricting nearly everything your sims can do. It is your job to keep your sims happy enough to rise in the ranks of their careers and lift the restrictions that make life so difficult for them. There are 20 unique restrictions that MUST be lifted and 6 restrictions that are optional. Hopelessness is lifted as soon as your founder clears the first restriction. Alien Technology and other Optional Clears do not have to be lifted in order to complete the challenge.
Good luck and get prepared for stinky, hungry sims for a generation or two or five!