In the progressive development towards 6G, the ROBUST-6G initiative aims to provide fundamental contributions to developing data-driven, AIIML-based security solutions to meet the new concerns posed by the dynamic nature of forth-coming 6G services and networks in the future cyber-physical continuum. This aim has to be accompanied by the transversal objective of protecting AIIML systems from security attacks and ensuring the privacy of individuals whose data are used in AI-empowered systems. ROBUST-6G will essentially investigate the security and robustness of distributed intelligence, enhancing privacy and providing transparency by leveraging explainable AIIML (XAI). Another objective of ROBUST-6G is to promote green and sustainable AIIML methodologies to achieve energy efficiency in 6G network design. The vision of ROBUST-6G is to optimize the computation requirements and minimize the consumed energy while providing the necessary performance for AIIML-driven security functionalities; this will enable sustainable solutions across society while suppressing any adverse effects. This paper aims to initiate the discussion and to highlight the key goals and milestones of ROBUST-6G, which are important for investigation towards a trustworthy and secure vision for future 6G networks.