Growth and remodelling are fundamental biomechanical processes that can be effectively described using the classical framework of continuum mechanics. These phenomena are typically modelled through the multiplicative decomposition of the deformation gradient tensor into a growth (incompatible) component and an elastic component. This approach introduces a fictitious intermediate configuration, representing a stress-free yet kinematically incompatible state obtained by applying the growth component of the deformation gradient tensor to the initial configuration. The elastic component subsequently maps this intermediate configuration into the final deformed state, which is kinematically compatible but generally associated with internal stresses and stored strain energy. Shell-like models offer an efficient way to simulate various biological systems, particularly those characterized by slender or thin-walled geometries. Examples include plant leaves, flower petals, insect wings, articular cartilage, and arterial walls. These systems are especially prone to mechanical instabilities, as they can relieve compressive stresses through out-of-plane deformations. Consequently, accurate computational modelling requires the development of morpho-elastic shell formulations capable of capturing these behaviours. This work presents an efficient and robust path-following analysis of growth-induced deformations and instabilities in thin biological tissues, based on large strain Kirchhoff-Love and solid-shell formulations. The use of NURBS basis functions, with their high continuity properties, enhances the accuracy of the numerical models and plays a critical role in the stability and performance of the proposed computational framework.