The digitalisation of healthcare has increased the risk of cyberattacks in this sector, targeting sensitive personal information. In this paper, we conduct a systematic review of existing solutions for data breach mitigation in healthcare, analysing 99 research papers. There is a growing trend in research emphasising the security of electronic health records, data storage, access control, and personal health records. The analysis identified the adoption of advanced technologies, including Blockchain and Artificial Intelligence, alongside encryption in developing resilient solutions. These technologies lay the foundations for addressing the prevailing cybersecurity threats, with a particular focus on hacking or malicious attacks, followed by unauthorised access. The research highlights the development of strategies to mitigate data breaches and stresses the importance of technological progress in strengthening data security. The paper outlines future directions, highlighting the need for continuous technological progress and identifying the gaps in the attack mitigations.