Name says what you have to do. All you have to do is complete 10 different characters mission modes story missions. You don't have to do all the other missions unless you want to. Check in the terminal for messages to continue or start the storyline if no more missions are available. Most characters have 5 story missions but I think some charcters might have less than 5 story missions. To do this quick and easily than you should do all the story missions on easy and you can use charcters that you have completed with official mode because they don't start at level 1 like everyone else.