The other answers that claim that "只怕" here means that "难事" is figuratively afraid of (i.e. can be overcome by) "有心人" are wrong. Here is an accurate translation:
Under the sky nothing is hard, but [I'm] afraid [it's about] people with the heart.
A loose English rendering could be:
It is never a matter that is hard, but a person's heart.
This construction "A，只怕B。", where "只怕" is not used in the other sense of "but only afraid of", invariably means that one has to be concerned about B when thinking about A. This is expressed idiomatically in English by "A, but I'm afraid B.", which is similar to the Chinese except that we add the "I'm". For examples taken from straight off the internet:
If you bite at and devour each other, [I'm] afraid [you] will be mutually destroyed.
Indeed [I'm] afraid those women are more and more uncontrolled; eventually if again [there] spread some words that damage the little prince's reputation, wanting to prohibit at that time, [I'm] afraid, is also too late.
To emphasize, in "A，只怕B。" it is always the speaker who is saying that he/she is afraid/concerned with something (often implying that the audience should be concerned too), never something in "A" that is afraid!
Side remark: "天下" is idiomatic for "in the whole world", but it actually reflects the historical worldview that we humans are restricted to what's under the sky/heavens. Since it is a universal notion across languages, the figurative expression can be retained.