Is shunning one's female cousin for more than eight months—due to her deviance and un-Islamic attire—considered a sin from a Sharia perspective, especially given that she is like a sister to the questioner?

The girl mentioned is a stranger to you unless she is a mahram (definition) to you through breastfeeding. Being close to her and mixing with her, even for help with studies, is a pretext for evil and corruption, because of the Prophet's (peace and blessings be upon him) saying: "I have not left behind me any fitnah more harmful to men than women," and "Beware of women, for the first fitnah of the Children of Israel was concerning women." Therefore, you should have avoided speaking to her to prevent fitnah. As for shunning her, it is not permissible for a Muslim to shun his brother for more than three days, unless there is a benefit, such as rebuking disobedient people and innovators. However, if shunning does not help in correcting her behavior, then another method should be used to reform her.