Until I learn something more nuanced, the way I distinguish consonants with ь after them is to try to pronounce them with my tongue up in the front of my mouth, almost touching the back of my teeth. This distinguishes it from the vocalized sounds that come when the tongue is well back in the mouth, as when English speakers pronounce words like "China". The position of the tongue like this very much affects vowels after it, and often vowels before it. If you try to say a "soft-sound" ch in "China", tongue up front, you end up with a very nasal quality with a kind of "eee" sound to the "i". It's almost impossible to say "China" normally (in English) with a soft-sound ch and the tongue right behind the teeth.
It would be simpler to understand if the Russian were stated as: «Это чья бода?» "This is whose water?"
That way, you can see that feminine чья attaches to feminine вода, while the generic "This (is)" stands before the phrase.
The thing that's hard for me to grasp is the fact that, although Это is pointing at вода, it's not sufficiently attached to it to require actual agreement - it's not the feminine Эта that you would use to translate "this water" = эта бода. It's like saying, "This [unknown thing] is whose water", even though you know exactly what the thing is.
It's not a sentence without a verb, and you don't have a verb. You also need a place-holder or null-pronoun like "this/it", which is normal in English, and seems normal in Russian, too, with the invariable это appearing so often. So, "This is whose water?" or "Whose water is this/it?"