In a multiplayer game, each instance of the ability affects only one defending player. For example, if you attack player A with two creatures and player B with two creatures, each of those players will lose 2 life, not 4.

In a Two-Headed Giant game, Campaign of Vengeance’s triggered ability has one defending player of your choice lose 1 life. The team doesn’t lose 2 life.

If a creature attacks a planeswalker, the defending player is the player who controls that planeswalker.