When the enchanted creature becomes tapped or is dealt damage, Cryoshatter’s last ability triggers. That creature will be destroyed when the ability resolves, even if Cryoshatter has left the battlefield or is somehow enchanting a different creature by then.

If the enchanted creature is tapped as a cost to cast a spell or to activate an ability that’s not a mana ability, Cryoshatter’s last ability will go on the stack on top of that spell or activated ability. Cryoshatter’s last ability resolves first (destroying that creature), then the spell or activated ability resolves.

Cryoshatter may target and may enchant a creature that’s already tapped. An ability that triggers when a creature “becomes tapped” won’t trigger until the creature changes from being untapped to being tapped.

If the enchanted creature is tapped as a cost to activate a mana ability, the mana ability resolves immediately, then Cryoshatter’s last ability goes on the stack.

A creature with trample blocked by a creature enchanted with Cryoshatter still needs to assign damage equal to the enchanted creature’s toughness (minus any damage already marked on the enchanted creature) before trampling over to a player, planeswalker, or battle.