how short does a female have to cut their hair to noticeably reduce the power of din against them?

Shalom, Thank you for your question. The idea that the way a person chooses to cut their hair will have an effect on the heavenly attribute of judgement, and how it effects a person, is certainly beyond the realm of normative Judaism. We believe that the way a person behaves, their keeping of Torah and Mitzvot, their constant building of good character traits, are the main things in G-d’s judgment of a person. The spiritual attributes of “din” and “chesed” that move in the world, and in a person’s life, are the result of many factors – both of the individual and of the time and place they live. Some of them can be affected by the individual’s personal level, and some come about through things that are not in a person’s control. However, none of this is related to such external actions as one’s choice of haircut. Any reference to this idea you may have read or heard of, is not referring to a person going to hair salon. At most you have misunderstood a kabbalistic reference that uses hidden and deep imagery to express ideas that should not be interpreted literally. At best they are symbolic. With this in mind, you would be best off continuing your religious growth through normative revealed Torah. Acts of loving kindness, keeping the mitzvot, working on one’s character. Many blessings.