1. She killed her.
2. She killed herself.
3. She looked at herself in the mirror.
4. She looked at her in the mirror.
5. You should take care of you.
6. You should take care of yourself.
7. He is very proud of himself.
8. He is very proud of him.
(Are they all grammatical? Which ones are not grammatical? #5 doesn't seem to be grammatical, right?)
2, 3, 6, and 7 are correct.
5 is incorrect.
The others are correct only if each direct object pronoun doesn't refer to the subject.