One of the alternate Asagis appears to be a Japanese Rhinoceros Beetle,
http://en.wikipedia.org/wiki/Japanese_rhinoceros_beetle. The only indications that the beetle is in fact an alternate Asagi would be the white-and-blue designs on its wings (which are identical to the designs on Asagi's jacket) and the furry neck-lining (also a feature of the jacket). Furthermore, though one would expect a giant beetle, Beetle Asagi is in fact the natural size for the particular insect, which may or may not lead to difficult targeting in battle.