The answer posted by Unrelated shows clearly that "repent of" is in far more frequent use than "repent for" in the Google Books database of published writing, but I don't think that the Ngram charts reproduced there offer a very useful head-to-head matchup of the alternatives. In hopes of remedying that shortcoming, I generated an Ngram chart for the period 1800–2000 for "repented of his" (blue line) versus "repented for his" (red line) versus "repented his" (green line):
This chart indicates that for the past two centuries the order of preference in published writing has been first "repented of his," second "repented his," and third "repented for his."
Similar graphs appear for "repenting of his" (blue line) versus "repenting for his" (red line) versus "repenting his" (green line):
and for "repent of his" (blue line) versus "repent for his" (red line) versus "repent his" (green line):
If you look at the individual Google Books matches that the line graphs are based on (which you can do here for the repented alternatives, here for the repenting alternatives, and here for the repent alternatives), you'll see that the form "repented/repenting/repent his" generates a higher number of false matches (such as "...truly to repent. His attitude...") than the other two forms. But even so, there are clearly more legitimate instances of "repent his" than of "repent for his."
Looking at the individual matches for the three forms ("repented of his," "repented for his," and "repented [no preposition] his"), I can't detect any difference in the intended sense of the verb based on the mediation of the preposition chosen (or omitted altogether).
Matches from the period 1934–2005 find that one person or another "repented of his" sin[s], cruelties, actions, violence, errors, evil deeds, act, love, harshness, early enthusiasm, selfish life, fears, opposition, haste, crime, former arrogant attitude, rebellion, worldly life, choice, wrongdoing, silliness, disdain, folly, disobedience, greedy ways, wickedness, work, and creation.
Matches from 1978–2005 find that a similar person "repented for his" birth, action, misconduct, love, act, sin[s], past deeds, hard work, folly, failure, transgressions, crime, selfishness, vanity, pride, behavior, evil conduct, wrong, and extramarital affairs.
And matches from 1953–2005 find that a person "repented his" love, sin[s], involvement, diatribe, first error, anti-music position, decision, political ways, crimes, bargain, eagerness, lack of hospitality, former conduct, past mistake, folly, action, command, and youthful devotion.
Those objects of repentance seem to me to be virtually interchangeable from one list to the next. That being the case, you should probably signal by other means any difference in meaning that you wish to convey with regard to repentance.