Core network slicing achieves flexible networking by combining virtualized network functions (VNFs). However, the failure of any VNF due to software and hardware failures will cause an interruption of the slice service. Since network slices share resources, a specific isolation mechanism is required to meet slice robustness demands. Most of the existing availability guarantee mechanisms focus on random VNF failures, and some of them involving external attacks rarely consider special isolation requirements of network slices. To realize slice availability guarantee under isolation mechanisms, this study proposes a method to guarantee network slice availability based on multi-level isolation. First, an availability guarantee model of core network resource awareness is built to meet the isolation requirements with consuming the least number of backup resources. Then, an isolation level assessment model is proposed to evaluate the isolation level of VNFs. Finally, a multi-level isolated backup algorithm (MLIBA) is proposed to solve the availability guarantee problem. In addition, an equivalent backup instance-based calculation method is put forward to address the PP-complete problem of availability calculation for a shared backup. Simulation results show that the proposed availability calculation method has high accuracy, and the introduction of multi-level isolation can double the robustness of slices. The comparison with existing studies shows that under the same isolation constraints and availability targets, the proposed method can reduce resource consumption by 20%–70% and increase the proportion of effective resources by 5%–30%.