What is the expiation for one who intentionally kills an animal?

There is no expiation (kaffara) prescribed by Islamic law for killing an animal, except for what applies to a person in a state of ihram (definition) for Hajj or Umrah (definition) if they intentionally kill game. In such a case, they are subject to a penalty, as stated in the verse: "O you who have believed, do not kill game while you are in ihram. And whoever among you kills it intentionally - the penalty is an equivalent of what he killed among the livestock, as determined by two just men among you, as an offering [to Allah] delivered to the Kaaba, or an expiation: the feeding of needy people or its equivalent in fasting, that he may taste the consequence of his deed. Allah has forgiven what is past; but whoever returns [to violation], then Allah will take retribution from him. And Allah is Exalted in Might and Owner of Retribution." It is not permissible to kill an animal without a valid purpose, except for what the Sharia (definition) has commanded to be killed.