Is there any way my opponent can prevent me from winning in this situation?
Considering only the cards mentioned, and assuming you chose the proper targets for the triggered abilities, your opponent is guaranteed to lose once you block with the Fiend.

The active player is the player taking the current turn [CR 102.1], not the player with priority or anything like that. So in that entire sequence, there is no way for your opponent's triggered abilities to go on the stack on top of yours. As mentioned in the question, both of your abilities go on top of the stack and each deals 1 damage to the opponent, so they lose before their own creature's triggered ability can resolve.