The Fang Bat Wing is an Event Item in Riviera: The Promised Land. It is received in the Aura Plateaus of Tetyth if certain requirements are met.
Acquirement: On the third screen of Stage 4, Area 5, go into Look Mode and examine the dark window. Throw a Rock if available to provoke the bat. From there, either choose to catch it, fail, and then defeat it in battle or choose to slash it and succeed to receive the Fang Bat Wing.
Function: Give it to NaNa of the Magic Guild in Crystal Cavern to be rewarded with a +30 HP stat boost for Ein.