Quantum Fisher information has recently been an essential tool for analyzing the phase sensitivity of the quantum states in various quantum tasks, requiring high precision, such as quantum clock synchronization, positioning and many applications which include quantum interferometers. Due to the interactions with the environment, all quantum systems are subject to various decoherence effects. Therefore the research on quantum Fisher information under decoherence has been recently attracting more attention. In this work, analyzing the quantum Fisher information, we study the phase sensitivity of bipartite quantum correlations, in particular four Bell pairs amplitude damping channels. For a specific Bell state we arrive at similar results of Greenberger-Horne-Zeilinger (GHZ) states (as expected). For the other three Bell states, we present our results which point the interesting behavior of quantum Fisher information with respect to the decoherence rate. We also find the regions where the quantum Fisher information exhibits discontinuities.