My idea is basically nobody takes ownership of the boss during the battle, only either the GM or the chosen RPer is in "charge" of deciding when the boss dies, and writes it out as part of their character's IC post.

A simple example of how it works:

Person A is the GM or player in charge of the boss
Person B is a normal player
Person C is a normal player

Person A roleplays their character normally, but also includes the boss's arrival to the scene, initial attacks or other actions
Person B roleplays their character normally, including any needed responses to Person A's character's actions, as well as the actions of the boss.
Person C roleplays their character normally, including any needed responses to Person A/B's characters' actions, as well as actions of the boss.
From this point onward, A/B/C each take turns posting their characters' actions and the boss's actions, until it's time for the boss to die, then Person A roleplays their character normally, and includes details on how all characters' actions play a part in ending the boss battle.

It's really a simple idea, and explaining it out just makes it look more complicated. Basically, just RP normally and include actions of other characters in your post if needed, without anyone RPing the boss specifically.