I think that Luffy completing his journey will achieve what every other Yonko wants (or at least one thing).
Big Mom: Luffy will destroy Fishman Island in the future, making it possible for the Fish-Men to live on the surface world free of persecution. So this will be a land where everyone can live happily and freely. It’s stated that one of Big Mom’s dreams is a land where everyone gets along.
Kaido: Luffy will have probably started the greatest war of the world since the Void Century, completing one of Kaido’s ambitions to start a war.
Shanks: This is just a suspicion based on what others have said, but one of Shanks’ dreams is to follow where his captain went. Only this dream was given to Luffy at the start of the series with the passing of the straw hat. So Luffy, by reaching Laugh Tale, will complete that dream.
Whitebeard: All he wanted was a family, and I would say the Straw Hats have already completed this through the way they act with each other. However it could extend to the Grand Fleet too.
Blackbeard: His is the only dream I’m unsure of, so I can’t make a guess here other than become recognized as Pirate King. But I also think that’s partially what Kaido and Big Mom want too.