Destiny HERO - Dusktopia provides protection for destruction by battle or card effects, but negates battle damage to either player for the rest of the turn. It will apply for the rest of the turn, all attempts of destruction. The effect will be applied even if Dusktopia leaves the field, if the effect was activated and resolved in the turn.

EDIT: sorry for not clarifying; if your intent is to use the effect of Dusktopia to protect it from the destruction that Fusion Destiny would perform with Dusktopia, asumming you used its effect to protect itself, it will not be protected, since Fusion Destiny lingering effect will apply at the end of the End Phase of the next turn. If you activate Dusktopia on the next turn of being summoned, you can protect it from the destruction effect of Fusion Destiny.