worth the trouble paused nearby [closed]
Solution 1:
One might group the parts of the sentence: "When [a limpkin or another bird he thought was worth the trouble] paused nearby..."
A simplified version of the entire paragraph is, "When a desirable bird landed within the hunter's range, he shot it."
That is, he doesn't shoot at every bird he sees, only those that are "worth the trouble", perhaps birds of a certain minimum size or value.