The development of critical data and artificial intelligence (AI) literacy has become a key focus in current discussions in Higher Education, thus it is necessary to develop and advance capacity building, reflectiveness and awareness across disciplines to critically address the possibilities and challenges presented by data and AI. In this paper, through an integrative use of the literature and the review of case studies and best practices in authentic and real world design, we propose a model that develops and enables critical data and AI literacies grounded in citizenship, civic responsibilities, and human centred values, rethinking how we develop knowledge and understanding in our disciplines, and also, in the value of our disciplines to society. The principles of data justice, which acknowledges the growing influence of data, its gathering, and use in society, promoting shared perspectives on how societal problems should be comprehended and addressed.These can provide a useful framework for authentic and real-world assessment design, bridging professional and discipline related knowledge with critical data and AI understanding in alignment with civic and citizenship literacies to examine the challenges we face by the impact of data AI on our societies and democracies. Our exploratory approach examines the relationship between authentic and real-world assessment design and critical data and AI literacy, using data justice as a catalyst for reflection and action to promote a deeper understanding of data and AI ethics through assessment practices that enable educators and students to confidently navigate the complex world of data and AI.