With my little one, now 3, I try very hard to help him see that if he doesn't like to be pulled on, or pinched, or yelled at or scared, others won't like it either. Any time he's caught, he gets a time out. Now, he really hates losing his playtime. So, after his timeout, I have told him something like, "Do you like to be hit/pulled/scared? (No) How does that make you feel? (sad) Then don't do it to (Fluffy). When you do what happens? (I don't get to play)."
Or, something like that. Sometimes I just take away something he really enjoys.
Sometimes it works. Sometimes he's after the animal whenever she's around.
He's also made the connection with Max in the book "Where the Wild Things Are" by Maurice Sendak. Max got sent to his room without supper because he was being mean and chasing the dog (not explained in words, but you can see it in the picture).
Hope this helps!