Hmm, maybe you're confusing "hledat" - "to look for" and "hlídat" - "to watch over, to guard"? Hledám svůj telefon (I'm looking for my phone), Hlídám tento dům (I'm watching over/guarding this house).
If "tu" is also a short for "tady" couldn't the sentence be translated as "who is looking for a cow here?"
It is a weird word order for an adverb of location. "Kdo tu hledá krávu?" would be much better.
Kráva is the nominative case form (subject), while krávu is the accusative case form (object). You've probably figured that out by now, but maybe this will help someone else who has the same question later. :-)
"Tu" in this sentence means we want to know who is looking for THE cow (the small black-and-white one, for example), as opposed to A cow (any cow at all).
Well, tu can often mean just that. "Kdo tu hledá krávu?" "Who is looking for a cow here?"
Are the hints supposed to just give you the solution right away?
Why is it wrong: Who searches the cow? Duolingo includes both of them: looking for and search.