Ion-beam therapy provides advances in cancer treatment, offering the possibility of excellent dose localization and thus maximising cell-killing within the tumour. The full potential of such therapy can only be realised if the fundamental mechanisms leading to lethal cell damage under ion irradiation are well understood. The key question is whether it is possible to quantitatively predict macroscopic biological effects caused by ion radiation on the basis of physical and chemical effects related to the ion-medium interactions on a nanometre scale. We demonstrate that the phenomenon-based MultiScale Approach to the assessment of radiation damage with ions gives a positive answer to this question. We apply this approach to numerous experiments where survival curves were obtained for different cell lines and conditions. Contrary to other, in essence empirical methods for evaluation of macroscopic effects of ionising radiation, the MultiScale Approach predicts the biodamage based on the physical effects related to ionisation of the medium, transport of secondary particles, chemical interactions, thermo-mechanical pathways of biodamage, and heuristic biological criteria for cell survival. We anticipate this method to give great impetus to the practical improvement of ion-beam cancer therapy and the development of more efficient treatment protocols.