This article addresses simultaneous faults in rotor motors and sensors of a quadrotor UAV. A robust fault-tolerant attitude control algorithm is proposed, integrating a generalized sliding mode observer (GSMO) with a composite continuous nonsingular terminal sliding mode (CCNTSM) controller to achieve high-precision attitude tracking and strong robust stability under multiple faults. To overcome the difficulty of distinguishing and reconstructing actuator and sensor faults, a state augmentation technique is adopted. Both types of faults are extended as augmented state variables, and an adaptive GSMO is designed. Through adaptive gain tuning and sliding mode compensation, the observer achieves synchronous decoupling and accurate reconstruction of various faults, including rotor motor and sensor faults. Based on the reconstructed fault information, a composite continuous fast nonsingular terminal sliding mode controller is designed. It adopts a nonlinear sliding surface, preserving finite-time convergence while effectively eliminating high-frequency chattering through adaptive gains and continuous switching functions. Simulations validate the effectiveness and robustness of the proposed method. The results show that, under three fault scenarios with increasing severity, the post-fault root mean square error of the roll channel is controlled within 0.031 3°. Under the compound fault involving complete roll angle sensor failure, pitch angle bias of 0.2 rad, and 40% pitch efficiency loss, the system maintains high-precision tracking. Compared with existing methods, the proposed method improves tracking accuracy by approximately one order of magnitude and reduces chattering energy by two orders of magnitude under extreme fault conditions.