On the Cryptic Totem it mentions: "While this creature is tapped, your opponent can't use the "shield trigger" ability of his shields."

If I break 2 shields with cryptic totem does the ability come into effect after its attack or when it attacks? Does the opponent get to use their shield trigger ability that instance?

Cryptic Totem is tapped before you break the shields.

Yes he deny shield triggers if he attacks because you tap your creatures before you attack.

The ability takes effect when the creature attacks, not when it breaks shields. So if you break two shields with this creature, your opponent won't be able to use shield triggers for the rest of the turn.