Chemotherapeutic agents for treating cancers show considerable side effects, toxicity, and drug resistance. To mitigate the problems, we designed nucleus-targeted, echogenic, stimuli-responsive polymeric vesicles (polymersomes) to transport and subsequently release the encapsulated anticancer drugs within the nuclei of pancreatic cancer cells. We synthesized an alkyne-dexamethasone derivative and conjugated it to N3-polyethylene glycol (PEG)-polylactic acid (PLA) copolymer employing the Cu2+ catalyzed "Click" reaction. We prepared polymersomes from the dexamethasone-PEG-PLA conjugate along with a synthesized stimuli-responsive polymer PEG-S-S-PLA. The dexamethasone group dilates the nuclear pore complexes and transports the vesicles to the nuclei. We designed the polymersomes to release the encapsulated drugs in the presence of a high concentration of reducing agents in the nuclei of pancreatic cancer cells. We observed that the nucleus-targeted, stimuli-responsive polymersomes released 70% of encapsulated contents in the nucleus-mimicking environment in 80 min. We encapsulated the cancer stemness inhibitor BBI608 in the vesicles and observed that the BBI608 encapsulated polymersomes reduced the viability of the BxPC3 cells to 43% in three-dimensional spheroid cultures. The polymersomes were prepared following a special protocol so that they scatter ultrasound, allowing imaging by a medical ultrasound scanner. Therefore, these echogenic, targeted, stimuli-responsive, and drug-encapsulated polymersomes have the potential for trackable, targeted carrier of chemotherapeutic drugs to cancer cell nuclei.