Pierce damage is dealt to "Avatar of the Seven Lands, Alice" at the same time as normal damage, effectively negating Pierce.
If multiple copies of "Avatar of the Seven Lands, Alice" are controlled by a player, their controller chooses which replacement effect happens.
If "Avatar of the Seven Lands, Alice" is dealt damage via its prevention effect, and an ability or effect triggers upon that J/resonator damaging a resonator (Ex.: "Beastly Attack"), then that ability triggers.
Note that this can be used to infinitely chain "Beastly Attack" or "Behemoth, the Earth Eater" triggers until all copies of Alice are either removed from the field or lose their abilities.