Polymeric nanoparticles (NPs) are commonly used as nanocarriers for drug delivery, whereby their sizes can be altered for a more efficient delivery of therapeutic active agents with better efficacy. In this work, cross-linked copolymers acted as core-shell NPs from acrylated palm olein (APO) with polyol ester were synthesized via gamma radiation-induced reversible addition-fragmentation chain transfer (RAFT) polymerisation. The particle diameter of the copolymerised poly(APO-b-polyol ester) core-shell NPs was found to be less than 300 nm, have a low molecular weight (MW) of around 24 kDa, and showed a controlled MW distribution of a narrow polydispersity index (PDI) of 1.01. These properties were particularly crucial for further use in designing targeted NPs, with inclusion of peptide for the targeted delivery of paclitaxel. Moreover, the characterisation of the synthesised NPs using Fourier Transform-Infrared (FTIR) and Neutron Magnetic Resonance (NMR) analyses confirmed the possession of biodegradable hydrolysed ester in its chemical structures. Therefore, it can be concluded that the synthesised NPs produced may potentially contribute to better development of a nano-structured drug delivery system for breast cancer therapy.