I thought of the adjective “soft” and its adverbial form “softly” and was not sure whether the adverbial form of the adjective “hard” was “hardly”.

Problem:
The most popular meanings of the adverb “hardly” are not the opposite of the adverb “softly”.

Explanation:
If you ask most Americans what the adverbial form of the adjective “soft” is, they very likely will respond that it is the adverb “softly”.

However, if you ask most Americans what the adverbial form of the adjective “hard” is, they probably will not respond that it is the adverb “hardly”.

From most to least popular, here are four definitions of the adverb “hardly”:

1. barely — as in “He hardly graduated from high school.”;
2. scarcely — as in “The news is hardly surprising.”;
3. with small likelihood — as in “She will hardly attend the wedding.”;
4. forcefully — as in “He threw the baseball hardly.”

So the fourth definition of the adverb “hardly” does go with the adjective “hard” in the same way that the most common definition of adverb “softly” goes with the adjective “soft” .

It is worth noting that — at least in American English — the first three definitions typically go with putting the adverb “hardly” adjacent to the verb, whereas the fourth definition typically goes with putting the adverb “hardly” adjacent to the object upon which the action is performed forcefully.

This gives us the solution.

Solution:
Use “He hit the ball hardly.” as a substitute for “He hit the ball forcefully.” Use “He hardly hit the ball.” as a substitute for “He barely hit the ball.”