As HybridPK's guide states, it's pretty simple. You just have to go online, and beat each of the Generals and Kingpins. This can all be at once, or it can be across 21 different connections with 21 different people. And it can be in Campaign mode or Time Trials. Doesn't matter!
Unless you have friends you can do this with, you're going to probably have a hard time finding people to play with to do it all in one sitdown, though.
So, first off, I recommend *NOT* resetting your gangs. Don't do it (unless you expect to want all 21 bosses back up and running after you complete this). Instead, try connecting with other players that don't have many of the bosses beaten (on the screen, it'll tell you how many generals they've defeated on their current game). Then just rock 'em out. You'll probably have to switch around to other people on occasion, unless you can actually find someone that hasn't defeated ANY of them yet. It's not too hard, though. Just takes some persistence and patience.
And since you're not doing it within your own game, you'll need a way to keep track of who you've defeated. That's easy. Here's a checklist!
Now go lay the smack-down, Agent.