Learn Croatian: Nemoj izgubiti taj divan ulov! - Don't lose that wonderful catch!

You're remembering a good general rule! Negative commands usually take imperfective verbs when giving a general prohibition, like telling someone they shouldn't ever lose things. However, when you are warning someone not to do a specific, single action at this exact moment—like losing this particular catch—you use nemoj with the perfective verb, which is izgubiti here.

Since taj divan ulov is the direct object, why didn't its endings change for the accusative case?

Because ulov (catch) is an inanimate masculine noun. In Croatian, masculine nouns and their modifiers only take the animate endings (like -a or -og) in the accusative case if they represent living beings. For inanimate objects, the accusative case is identical to the nominative case, which is why taj divan ulov looks exactly like a subject.

Why does the sentence use the indefinite adjective divan instead of the definite form divni?

When a masculine adjective is in the accusative case for an inanimate object, the indefinite form (divan) is typically used to describe the quality of the noun. The definite form (divni) would strictly mean "the wonderful," but since the demonstrative pronoun taj (that) is already specifying exactly which catch we mean, adding a definite adjective would be redundant.

How does the noun ulov relate to other vocabulary for hunting or catching?