First, before loading a game, make sure "Soft Reset" is enabled - press the right-shoulder button to toggle the little green indicator in the top right corner of the bottom screen on or off.
Then, in the game, press the L and R and X and Y and A and B buttons at the same time to reset.
This doesn't work on all games, but it does on most.
Also, be careful not to mash buttons that way in the R4 menu - if it sees an "X" button press, followed by an "A" button press, it'll assume you want to delete the currently selected item.