I was playing around in minecraft and found out that if you shoot an arrow at a bat hanging upside down, you can kill it by shooting lower than the bat.
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Arrow + Bat is what it would look like with the arrow and bat together

I would add a video but it was too big to attach

Confirmed.
The hitbox of the bat goes down to the bottom of the block and the hitbox of the arrow is way bigger than the arrow itself, see screenshot.
If both hitboxes meet, the hit counts.

Confirmed for 1.7.5, 1.7.9 and 14w11

Confirmed for 1.8.