The controller of Heart-Piercer Bow chooses the target of the triggered ability. Heart-Piercer Bow is the source of the damage, not the equipped creature.

The triggered ability resolves before blockers are declared.

In some rare cases, a Heart-Piercer Bow you control may be attached to a creature that’s attacking you or a planeswalker you control. In that case, you choose the target of the triggered ability, but as you are the defending player, you must choose a creature you control as the target.