For example, this idiom is a thing that I'm trying hard to find. It applies itself in this situation.
While the idiom needle in a haystack is pretty close, it only describes the state of being hard to find, not the effort you actually have to spend to find it. It might be easily found by most people, but not me. That thing can be an object, an job, or a coterie.
More specific, the thing I'm looking for is a field of academic. For a long time, I have always wanted to see myself to do a specific scientific activity. But only recently I find the exactly name of the field that I think I should work for. Without it, my academic proposal is less persuaded. I want to convey this joy of this little success into my essay. Thanks to many answers, I think look high and low for is what I need, since it's simple enough so that the readers won't think that I'm trying to use bombastic words.