The time-varying multipath introduces major distortions to transmissions in the underwater acoustic communication channel. Channel estimation is often used as one of the central steps to address such distortions in high-rate communication receivers. The focus of this paper is to quantify the impacts of the channel fluctuations on the performance of the least-squares channel estimator. A metric, channel variation ratio (CVR), is defined to describe the rate of fluctuations in the channel impulse responses. Equations are derived to reveal the direct relationships between the CVR and channel estimation performance, which is measured by the channel estimation mean squared error (MSE) and signal prediction error (SPE). The equations show that both the MSE and SPE increase linearly with the CVR. The MSE and SPE metrics both have an error floor for time-varying impulse responses, even with zero ambient noise. It is confirmed that an optimum estimated channel length, achieving the minimum estimation error, exists for time-varying impulse responses. The truncation effects in the channel estimation are also investigated. Experimental data are used to validate the findings.