A. The mitzvah of bestowing chessed extends to both a person whom one loves and a person whom one hates.
B. It goes without saying that if one hates the other person without justification [i.e., in violation of Torah law] — for example, he did not do some favor for you — then it is certainly forbidden to withhold any favor from him. In this case, if the favor was in fact withheld, then besides violating the positive commandment of Gemillus Chasadim, one would also transgress the negative Torah commandment of Do not take revenge and do not bear a grudge. But even if that other person is hated because there is a mitzvah to hate him (such as you saw him commit a sin that all Jews know is forbidden), even so it is a mitzvah to do chessed-kindness for him when he needs it.