I checked social media and saw someone spoke something badly behind my back to her followers (she has like 1000 followers) without telling me. Is it possible to share screenshots of her tweets to my followers?
Backbiting (...speaking about a Muslim in his absence and saying things that he would not like to have spread around or mentioned Islam Q&A) is a sin in Islam and the punishment is described in Surah Al-Humazah (Qur'an 104). Engaging in backbiting out of revenge does not make it better. In fact, a Qibla.com fatwa highlights this as one of the reasons people engage in backbiting:
Causes of ghibah
- Thirst for revenge. Backbiting one’s brother and obtaining gratification from his anger. ...
Qibla.com, sourced from IslamQA.org
The fatwa continues to list exceptions when backbiting is permissible. Relevant here are:
(2) Seeking help to change an evil, or to reform the wrongdoer. If the intention in telling the ghibah is not to change the wrong, then it is forbidden to relate it.
(4) Warning, such as warning a prospective buyer that the merchant is a swindler, or warning a student that his prospective teacher is an innovator or a deviant.
(6) Someone who sins openly, and has no qualms about his sins being mentioned.
You can decide for yourself (or with someone knowledgeable) if one of these apply in your particular case.
I acknowledge that it's plausible that backbiting online might be different, since it is possible that the person who is being backbitten might actually see the post, and therefore it's not behind their back. (I even asked about this once; see Is backbiting from an anonymous online account still backbiting? but it hasn't got a good answer yet.) However, it seems unrealistic to think that makes it okay. The punishment may even be worse due to the large-scale nature of backbiting online.