Accomplishing eternalism would mean always knowing the fixed meaning of everything, and acting accordingly. That is impossible, because there are no fixed meanings. It’s also not possible to completely blind yourself to nebulosity, and not possible to always give in to the insane demands of supposed fixed meanings.
Mainstream Christianity recognizes this, actually, with the doctrine of original sin. It is not possible for humans to avoid sin. Everyone is sometimes in conflict with eternal meaning.
Some eternalist religious sects (typically termed the “mystical” branches) claim that accomplishment is possible. You can perfectly unify your self with the Cosmic Plan while in this life. This usually implies monism, and I’ll discuss such mysticism in detail in the monist chapter of Meaningness.
Some eternalistic political ideologies claim that collective accomplishment is inevitable; history guarantees utopia, eventually. Some non-political eternalist progress ideologies (versions of transhumanism, for instance) also say that accomplishment is at least possible in principle.