MTG Salvation

I block a trampling Zurgo Helmsmasher with Heliod, God of the Sun and Erebos, God of the Dead, my opponent casts Boros Charm to grant Zurgo double strike so he could trample more damage through.

Under normal circumstances, a blocking creature killed by first strike would not allow the DS creature to hit a second time, so is it possible to sacrifice both gods just so Zurgo cannot hit a second time?

Because Zurgo has trample you cannot stop zurgo from dealing the normal combat damage after the first strike damage.

From the comprehensive rules:

702.19c If an attacking creature with trample is blocked, but there are no creatures blocking it when damage is assigned, all its damage is assigned to the player or planeswalker it’s attacking.

Quote from NoobinCube »

Because Zurgo has trample you cannot stop zurgo from dealing the normal combat damage after the first strike damage.

From the comprehensive rules:

702.19c If an attacking creature with trample is blocked, but there are no creatures blocking it when damage is assigned, all its damage is assigned to the player or planeswalker it’s attacking.

I see, so if there's no trample, then double strike damage won't go to the defending player, but because he has trample at that moment, his double strike will still apply after the blockers are dead.

Correct. You can only remove Zurgo or prevent the damage with a damage prevention effect like, for example Awe Strike to avoid getting the damage.