This study focuses on the topic of distributed adaptive cooperative tracking control (CTC) for non-strict feedback multi-agent systems (MASs) including input unmodeled dynamics, prescribed performance, sensor faults and unknown control directions. An adaptive neural CTC tactic is raised via command filtered backstepping technique. With the help of the property of Gaussian function, the barriers produced by the non-strict feedback terms and partial sensor faults are handled. Moreover, the prescribed performance on measured synchronization error is considered by designing a finite-time performance function. By introducing normalization signals and adjusting parameters, the problems caused by input unmodeled dynamics are resolved. The compensation signals and normalization signals are integrated into the whole Lyapunov function in the stability analysis. All the variables in the controlled system are turned out to be semi-globally uniformly ultimately bounded (SGUUB). Meanwhile, the synchronization errors never exceed to predefined boundary. A simulation example is employed to confirm the viability of the constructed control method.