We present the results of the near-infrared (NIR) to mid-infrared (MIR) slit spectroscopic observations of the diffuse emission toward nine positions in the nearby irregular galaxy Large Magellanic Cloud (LMC) with the Infrared Camera (IRC) on board AKARI. The unique characteristic of AKARI/IRC provides a great opportunity to analyze variations in the unidentified infrared (UIR) bands based on continuous spectra from 2.5 to $13.4{mu}m$ of the same slit area. The observed variation of $I_{3.3}/I_{11.3}$ suggests destruction of small-sized UIR band carriers, polycyclic aromatic hydrocarbons (PAHs) in harsh environments. This result demonstrates that the UIR $3.3{mu}m$ band provides us powerful information on the excitation conditions and/or the size distribution of PAHs, which is of importance for understanding the evolutionary process of hydrocarbon grains in the Universe. It also suggests a new diagnostic diagram of two band ratios, such as $I_{3.3}/I_{11.3}$ versus $I_{7.7}/I_{11.3}$, for the interstellar radiation conditions. We discuss on the applicability of the diagnostic diagram to other astronomical objects, comparing the LMC results with those observed in other galaxies such as NGC 6946, NGC 1313, and M51.