There are two dog deaths and one dog injury.
The dogs are left chained up and the owners can't get back to them. All of the dogs manage to break loose except the oldest dog, who is too weak. They show him lay down and close his eyes and later in the film, the owner finds his body still chained up.
Another dog falls off a cliff and is injured. It dies overnight. There's no blood or anything. It just lays down and whines.
The third dog has her foot injured by a leopard seal. There's one scene where they try to make you think she's dying, but she's found later and rescued.