Shear-horizontal surface acoustic wave (SH-SAW) filters have shown strong potential for low-loss, compact, GHz-frequency RF front ends. In this work, we demonstrate a high-performance SH-SAW filter design at 4.35 GHz utilizing 42°Y-cut thin-film lithium tantalate (LiTaO3) on a SiO2/Si platform. Despite the limitations of thin aluminum metallization and its associated ohmic losses, we show that implementing a Bartlett window apodization technique, primarily intended for in-band spurious-mode suppression, yields a significantly improved quality factor (Q) of 1,522 from 688 in conventional interdigitated SH-SAW resonators. This enhancement enables a third-order ladder filter at 4.3 GHz with an insertion loss of 1.59 dB, compared with 1.65 dB for a conventional SH-SAW filter. In addition, our filter with apodized resonator designs achieves a 3 dB fractional bandwidth (FBW) of 3.24% and out-of-band rejection exceeding 14 dB, all within a compact footprint of 0.4 mm2. These results suggest that apodized thin-film LiTaO3 designs are highly promising for low-loss, miniaturized, cost-effective radio frequency acoustic solutions in next-generation communication and sensing applications.