As soon as you start to cast Worldheart Phoenix from your graveyard, the card moves onto the stack. At that point, it's too late for an opponent to prevent you from casting it by removing it from your graveyard.

If you cast Worldheart Phoenix this way, it is a spell and can be countered.

Casting Worldheart Phoenix from your graveyard by paying its alternative cost doesn't change when you can cast it. You can cast it only at the normal time you could cast a creature spell.