Achilles, the destroyer of men
This title, "Destroyer of men" is exactly what fits "losing someone" because Achilles was indeed a man slaughterer, and that is hand in hand with loss for not only the families of those men but also the loss of Achilles's humanity.
[ Atlas ] stands immovably upholding the wide heaven upon his head and unwearying hands
Atlas losing his freedom, punished to eternally hold up the heavens, this shows losing something Humanity and myself personally consider extremely important. Poor Atlas.
but the others blow fitfully upon the sea. Some rush upon the misty sea and cause much destruction for men with their evil, raging blasts;
This shows a form of losing stuff, in this case, lives, materials, families. The gods are taking from humanity out of spite or anger, maybe even "fun", and its very important in showing the relationship between the gods and mortals.
the cry of both armies as they shouted reached to starry heaven; and they met together with a great battle-cry.
A great loss, indicated not directly but with war, comes bloodshed, and with these words we can see both sides were ruthless and wanting blood. This is significant because it shows that with the fight they were willing to give their lives for both sides' objectives.
And he was reigning in heaven, holding the lightning and glowing thunderbolt, after he had overcome his father Cronus by force;
While this is referring to not "recent loss" Hesiod still refers to Cronus's loss to Zeus of kingdom and home. This is significant just because of the impact Zeus's rule had. Without Zeus we would be lacking almost all the gods or at least those gods in they key positions, like Hades being the god of the dead.