Many optoelectronic processes in colloidal semiconductor nanocrystals (NCs) suffer an efficiency decline under high-intensity excitation. This issue is caused by Auger recombination of multiple excitons, which converts the NC energy into excess heat, reducing the efficiency and life span of NC-based devices, including photodetectors, X-ray scintillators, lasers, and high-brightness light-emitting diodes (LEDs). Recently, semiconductor quantum shells (QSs) have emerged as a promising NC geometry for the suppression of Auger decay; however, their optoelectronic performance has been hindered by surface-related carrier losses. Here, we address this issue by introducing quantum shells with a CdS-CdSe-CdS-ZnS core-shell-shell-shell multilayer structure. The ZnS barrier inhibits the surface carrier decay, which increases the photoluminescence (PL) quantum yield (QY) to 90% while retaining a high biexciton emission QY of 79%. The improved QS morphology allows demonstrating one of the longest Auger lifetimes reported for colloidal NCs to date. The reduction of nonradiative losses in QSs also leads to suppressed blinking in single nanoparticles and low-threshold amplified spontaneous emission. We expect that ZnS-encapsulated quantum shells will benefit many applications exploiting high-power optical or electrical excitation regimes.