This paper investigates a practical time-varying formation control method for quadrotors subjected to disturbances, uncertainties, and switching-directed topologies. A fully distributed formation control scheme is proposed using a linear-velocity independent position controller (LVIPC) and a nonsingular terminal sliding mode attitude controller (NTSMAC). A distributed observer is adopted to eliminate the measurement of linear-velocity states, and only local neighbor states are needed to realize formation flight. A time-varying nonsingular terminal sliding mode manifold is designed to suppress the reaching phase and ensure the finite-time convergence. Adaptive estimators are employed to remove the reliance on the prior knowledge of the upper bound of lumped uncertainties. It is then proven that all the closed-loop signals are bounded under the proposed method. Comparative experimental results based on a practical outdoor hardware solution are presented to confirm the effectiveness of the suggested control algorithm.