1) Complete waste of time 2) Foolish errand 3) Fruitless errand 4) Frustrating quest 5) Futile activity 6) Futile pursuit 7) Futile search 8) Useless search 
A wild goose chase is a colloquial expression originally for an erratic course taken by someone followed by someone else, and now for a fruitless or hopeless quest. the expression comes from the difficulty experienced in catching a wild goose (properly a greylag goose).
[n] - the fruitless pursuit of something unattainable
noun the fruitless pursuit of something unattainable