Why does this character look like this after the treatment?

Pascal Laugier on their approach to realism:

I really wanted all my effects to be almost medical. To be as realistic as possible because the film is not a rollercoaster, it's supposed to be about the flesh, the real condition of the body when you hurt yourself, and you know in real life when you torture your body it's already impressive enough not to need you to go over the top. So what you see now on screen could be really true. We even used some medical documents that we took from real life to keep it as realistic as we could.

Anna's chest looks as if modified radical mastectomy had been performed. The definition from Johns Hopkins (another source with a good illustration showing what's removed):

The entire breast is removed. This includes the nipple, the areola, the overlying skin, and the lining over the chest muscles.

In the making of video

the skin costume is shown and the pectoralis major is visible so it was not supposed to be removed (no radical mastectomy). The tissue doesn't appear to be injured, so it was not a hack job.

But why did they do it this way?

Two analyses, conducted from different angles, come to a very similar conclusion:

To deindividualize the martyr.

1) Feminist side

There is a scientific paper about it, but I can't access it:

_{Amy M. Green PhD (2011) The French Horror Film Martyrs and the Destruction, Defilement, and Neutering of the Female Form, Journal of Popular Film and Television, 39:1, 20-28, DOI: 10.1080/01956051.2010.494187}

However, a blog article by Athena Genevieve (Violent and Vile Women in Excision and Martyrs: Feminism in Modern Horror Films) cites it:

Anna is never “sexualized” (Green 22) during her torture. Rather through the destruction of her body the audience witnesses “gender regression” (Green 24) as opposed to eroticization. Like the other victims, so brutalized they appear “barely human” (Green 21), Anna becomes “increasingly less identifiable as female” (Green 24). It is in the “skinning…and final neutering” (Green 25) that Anna ceases to appear to be a woman at all, with her “breasts and external genitals removed” (Green 25).

Athena notes:

The film forces the audience to examine human cruelty and vulnerability beyond the usual parameters of gender and sexuality.

In this regard, it's interesting what Pascal Laugier said in interviews. To Rob Carnevale from indiLONDON:

I wrote it on a very first-degree level. I felt very close to what my characters are living in a metaphorical way. I have no distance from this film. It’s very personal.

and to Lee Griffiths from Eye For Film:

It’s not a film about torture. It’s a film about suffering. I really needed the audience to feel the pain, to reach our limits, so maybe it would reach another level after the pain, like my main character does, reaching some transcendent state.

2) Plot-wise

This is taken from Simon Abrams film review for Slant Magazine:

The “other side” can only be reached, according to Lucie’s captors, by victims of violence that is so extreme that they can no longer perceive the mundane world. They must be young and they must be female (so says the older woman organizing the experiment). These “martyrs” can no longer see people (let alone their race), but to reach that point of transcendence, they have to first undergo a process of “other"ing, which in this case involves non-stop beatings.

and

These girls must first be completely alienated and once they’ve been physically and emotionally broken down, they have their “other"ness and all other traces of their identity forcibly ripped away from them. This means literally losing their skin, the flesh ripped away to reveal glistening tendons and muscles. Any possible sign of their race or gender is thus completely removed, turning them into so much unidentifiable flesh. First the martyr becomes an “other,” then they become nothing.

Conclusion:

This was not a mistake by the filmmakers, but intentional. It was also intentional by the captors. Pascal Laugier wants us to feel what the main character(s) feel. The captors want the martyr to reach that state of transcendence, for which they have to give up everything in this world and become one with the pain and suffering.

From Human Breasts

The breast is the tissue overlying the chest (pectoral) muscles. Women's breasts are made of specialized tissue that produces milk (glandular tissue) as well as fatty tissue. The amount of fat determines the size of the breast.

So breasts is only some tissues, so skinning will remove any tissue in human body, in case women body it may remove breasts too. There is no bones in breasts.

As you might expect, peeling the skin off of an entire human being is kind of a difficult task.