If Demigod of Revenge is countered *before* its triggered ability resolves, the ability will still resolve. It will return that Demigod of Revenge from your graveyard to the battlefield, as well as any others. If you’re casting a spell to counter Demigod of Revenge, it’s important to clarify you’re casting it *after* the triggered ability resolves if you don’t want that Demigod of Revenge to be put onto the battlefield.

The triggered ability will resolve before Demigod of Revenge will.

This ability triggers when you cast Demigod of Revenge as a spell. It won’t trigger if Demigod of Revenge is put directly onto the battlefield.