(Please note that a character gets a "kill" for killing a named person or causing a death.)
Non-canon deaths
If Bigby fails to save himself during an action scene, then there will be a scene where he dies, and the player gets a game over screen. However, the player can try again from that checkpoint, and Bigby can re-spawn. These are the characters that can kill him in the game if Bigby doesn't stop them.