We developed a new simplified method for the synthesis of well-defined linear, diblock, or starlike N-(2-hydroxypropyl)methacrylamide (HPMA)-based polymer drug carriers using controlled reversible addition-fragmentation chain transfer polymerization. The prepared monodispersed polymers are after the drug attachment intended for enhanced anticancer therapy. This new approach significantly reduces the number of required synthetic steps and minimizes the consumption of organic solvents during the synthesis. As a result, highly defined linear, diblock, and starlike copolymers designed for pH-triggered drug activation/release in tumor tissue were formed in sufficient amounts for further physicochemical and biological studies. Within the synthesis, we also developed a new procedure for the selective deprotection of tert-butoxycarbonyl hydrazide and amine groups on hydrophilic HPMA copolymers, including the one-pot removal of polymer end groups. We studied and described in detail the kinetics and efficacy of the deprotection reaction. We believe the simplified synthetic approach facilitates the preparation of polymer conjugates bound by the pH-sensitive hydrazone bond and their application in tumor treatment.