The seemingly easiest way to force fumbles is through blocking punts. As always, turn off the penalties and position your defender directly in front of the opposing QB while being careful not to touch any other defenders in the process. Sack him three times (or otherwise stymie the play), to force the AI into a punt situation.
Select the Block Punt formation (other formations seem harder for this to work, but the Block Punt works almost every time) and position your defender directly in front of the punter. As soon as the ball reaches him, hammer him and the ball will either knock loose, or it may hit you before it reaches him and still count as a fumble.
After forcing 4 fumbles in this way, the Achievement will unlock.
Try this during a season mode game, and you can continue onward to unlock the Butter fingers Achievement after three more fumbles (7 total).