Bergelmir was the frost giant grandson of Ymir, the first frost giant, who along with his wife were the only giant survivors of the enormous deluge of blood which flowed from Ymir's wounds when he was killed by Odin and his brothers Vili and Vé. According to the Gylfaginning, the two escaped the flood of blood and subsequently became the progenitors of a new race of frost giants.
They sailed for weeks until they found new land. Bergelmir called it "Jötunheim", a realm where the Giants served no master but themselves. Bergelmir and his wife proceeded to repopulate their race and ruled benevolently over the Giants as King and Queen.
Bergelmir never sought vengeance against Odin for the murder of Ymir or the near-extinction of his race, choosing to prosper instead. He eventually died of old age, surrounded by people who loved him.
Mimir: "If I'm not mistaken, we've yet to discuss the tale of the Giant Bergelmir... "
Atreus: "Oh yeah... I remember his shrine. It looked happier than the other ones... mostly."
Mimir: "... it begins in an ocean of blood!"
Kratos: "Finally. A story worth hearing."
Mimir: "If you remember, Ymir, the First Giant, was fatally stabbed by Odin. It's in his blood our story starts. Ymir's magical guts poured out in a torrent so violent it threatened to flood all of creation. The Jötnar were unprepared, as the very last of them where washed away in the endless tide. Not just Ymir, but all of Giant-kind faced extinction. And so would Odin's victory had been complete. But... Ymir's kind did not all perish that day. Staying afloat in the hollowed husk of a tree, the Frost Giant Bergelmir endured, as did his lady wife. For weeks they sailed, until finally they came upon a new land. They called it Jötunheim, and there they would start anew. As father and mother they would multiply exceedingly, and as King and Queen they worked to make Jötunheim a land where Giants would know no master but themselves. Bergelmir never sought revenge for Odin's slaughter. His vengeance was to live and prosper. He died at peace, a legion of his kin to mourn him. He would ever be known as Bergelmir the Beloved."
Atreus: "'Bergelmir the Beloved'... huh... I've never heard a story end that way. Not a true one anyway."
Mimir: "Few do, laddy."