Who attempts to break up the quarrel between Achilles and Agamemnon?

The person who attempts to break up the quarrel between Achilles and Agamemnon is Nestor, the wise old king of Pylos.

He is a respected elder and mediator who tries to reason with both men and find a compromise. However, his efforts are ultimately unsuccessful, as both Achilles and Agamemnon remain stubborn and unwilling to yield.