It's a reference to baseball. You need to swing the bat just right -- too hard can be as bad as too soft. Actually, I'm not that good at baseball, but it's a common American expression.

More context would have been helpful--next time consider giving more. I found the whole paragraph by Googling. It is about U.S. Democratic party presidential hopeful, Hillary Clinton: "But it also appeared to reflect the thinking of campaign operatives and outside groups that are looking past the Republican primaries and toward a general election race against a woman who has often benefited from rivals who swung too hard." It's a baseball metaphor. A hitter can be cautious, and try to swing accurately in order to get a "hit" and run to first base. A "hit" is good. A hitter can "swing for the fences." This means swinging very hard. If the bat hits the ball accurately, the ball will fly completely out of the ball field. The hitter will get a "home run." This is dramatic and exciting and usually results in a big score. A home run is better than a hit. It's hard to hit a home run. A batter who tries to hit a home run may fail and be put "out." A home run is better than a "hit," but a "hit" is much better than being put out. Depending on the score and the game strategy, it might be wiser for a batter to try for a hit than to swing too hard, trying to get a home run, and miss. According to the article: Some of Hillary Clinton's opponents are "swinging very hard" by making very strong attacks. Donald Trump said "The fact is that what she has done is criminal." "Swinging too hard" could backfire. If voters don't think that Hillary Clinton deserves to be called "a criminal," they might get angry at Trump and sympathize with Clinton. "Many other prominent Republicans, however, were more restrained." They don't want to swing too hard, because "in the past Hillary Clinton has often benefited from rivals who swung too hard."

It could also reference tennis or boxing. It means if you try too hard, it often causes you to fail!