This achivement is pretty staright forward. All you have to do is complete 5 different characters mission modes story missions. Story missions only, so you don't have to complete the other missions unless you want to. Each character usually has 5 story mission but some charcters I think have less than 5. Also check in the terminal to see if there is a dialogue to unlock a new mission because this is usually the case if you can't do anymore or to start story missions. If you want to do this quick then you should do them all on easy and if you beat official mode with characters than you should use them because they won't start at level 1.