The solution below (thanks ssssssssssssss1) for the Billy the Kid achievement works quite well. In short, start a tournament with one player and one bot and change the advanced settings (Lives to 1, Combo limits to Triggers Only, Allow Repeat Buttons to No and Wrong Button Penalty to 0) and select an easy difficulty. Select Juan Aguacate for both players as that character has no dialogue, which speeds things up considerably. And then go through the duel and select Rematch over and over.
For Jesse James, you probably already have won a fair number of duels already if you went through the Skill Tester and a few tournaments. It took me less than 10 minutes of grinding to win my 50th duel.