In this paper, we propose and design a chalcogenide (As2S3)-based slot waveguide taper with exponentially decreasing dispersion profile to realize high-degree pulse compression of low-power chirped solitons. Based on the waveguide taper designed, pulse compression of fundamental solitons, and chirped 2-soliton breather are both investigated numerically. With self-similar pulse compression scheme, a 1 ps input pulse is compressed to 81.5 fs in 6 cm propagation. By using 2-soliton breather pulses, a 1 ps chirped pulse is compressed to 80.3 fs in just 2.54 cm. This is the first demonstration of the feasibility of high-degree nonlinear pulse compression in As2S3-based slot waveguide taper.