Here's my way of gaining more than +50 fame a minute, which can be done as soon as you get into Mexico.
At Casa Madrugada, buy the property there (in case you die). Equip the elegant suit, which enables you to cheat at poker. In Casa Madrugada, there's a poker table for $50, so go to it and start a game of poker. As soon as you start dealing, press Y to cheat. If you don't balance the arrow at all, you'll fail and be caught cheating. This will lead to a duel. Winning the duel will get you +50 fame.
Go back inside the saloon to the poker table, rinse and repeat. I got +350 fame this way in just ten minutes.
Also, if you're aiming for the chilvary's dead side of this achievement, this little town is a great place for it, as you can kill all the citizens there, gain minus honor per kill, and no one will even try to report you for your crimes (some will fight back, but it's easier than fighting law enforcement).
EDIT: winning the duel by disarming your oponent rather than outright killing him with nets you +100 fame per duel... I've found that killing him via multiple shots to the face is less risky, though.