Don’t trash her* or get too hostile with her. I have a feeling that she has some pretty major insecurity/shame issues.
People who bully tend to have some issues related to shame. (I’m sure we’ve all heard the comments that bullies have low self-esteem and that is what leads to the bullying.) So, with that in mind, don’t try to give this person a hard time. Don’t try to add to her shame. Clearly, she is having some kind of issue that leads her to act in such a way. Just remember that as bad as her comments may be, she is a person and she deserves as much respect as you do.
Don’t let her make you feel angry or ashamed or anything. And don’t try to make her feel ashamed either. She obviously made the posts to get the attention of the fandom and to make the fandom feel bad, but that doesn’t mean that you have to go back at her.
If you want her posts to stop, then report her to Tumblr. If you don’t want to do that, then just block her on here. If you still see things that she says, then scroll past them. (I’m sure that we all do that from time to time.)
Since her posts contain images from thinspiration sites, then I would say that you are probably looking at a girl who has a negative body image and thinks of herself as being “fat” or “bad” or “wrong” in some way. She is probably tearing down members of the fandom and stereotyping them as being “fat” or “ugly” or “disgusting” because she sees the fans as “weak” in the same ways that she feels she is weak. She may even feel that the fans are weaker. Even if she doesn’t, she’s trying to help boost her own ego by making these posts. So don’t encourage the posts by attacking her. That will only make it worse.
*I’m assuming it is a girl because I haven’t seen many guys who readily link to pro-anorexia images and sites.