Atomically thin two-dimensional (2D) semiconductors are extensively investigated for optoelectronic applications that require strong light-matter interactions. In view of such applications, it is essential to understand how (photo)excitation alters the non-linear optical response of these materials under high carrier density conditions. Broadband transient absorption (TA) spectroscopy is by now a widely used tool to study the semiconductor physics in such highly excited systems. However, the complex interplay between different many-body interactions in 2D materials produces highly congested spectral information and an ensuing non-trivial non-linear photo-response, thereby masking the desired intrinsic photophysics. Herein, we outline a concise roadmap for analyzing such congested datasets based on examples of TA analysis of various 2D materials. In particular, we emphasize the synergy between an initial qualitative understanding of the transient photo-response based on line shapes and their derivatives and a consequent quantitative spectral deconvolution backed by such insights.