As a writer, ChrisOwens is probably referring to the fact that it is often difficult to think of ways that the protagonists could overcome a really formidable adversary, and thus it is tempting to make the antagonist seem dangerous except for some fatal weakness which the hero conveniently discovers.
The answer is that it isn't the story that has Paper Tiger Syndrome, it is the author.
You might compare it to the phrase "Quaker cannon," which could be used either by the group / person making the threat or the group / person facing the threat.
According to Marion Zimmer Bradley, in 'What is a Short Story?', she writes:
[The odds are NOT INSUPERABLE ENOUGH, or the reader does not believe they are sufficiently insuperable. If your hero/ine goes out to fight a bear, it must not turn out to be a teeny-tiny bear cub he could put in his pocket and take home for a pet. The reader must have a REAL PROBLEM. A FAKE PROBLEM is also known as a "paper tiger."]
As an aspirer (can't claim the writer label yet), I found her formula interesting: A LIKABLE CHARACTER overcomes ALMOST INSUPERABLE ODDS and BY HIS OR HER OWN EFFORTS achieves a WORTHWHILE GOAL.
So, of course, as I'm trying to polish up a story to send out, I'm plagued with another doubt. Oh, I could say, well my character is overcoming doubts, learning to step into a leadership role, and this is his first command decision. My point is to show how he's grown into the role not to show an intense battle scene.
But then, that might not really fly with a first reader according to the mini-Survivor on one of my shoulders.
You can do this easily enough by having him make a fool out of himself earlier in trying to deal with subordinates without a sense of confidence and authority. Then, as we approach the critical scene, we have reason to believe that he'll flub it again, he has reason to believe that he'll flub it again, and since he's prone to self-doubt he's probably torturing himself with all the probable horrible consequences of the fact that he's going to flub it.
Of course, then you need to find a realistic way of having him overcome his anti-self in time to do what he needs to do. That's always very difficult, the human mind is a murky place, and in real-life people do the strangest things for even stranger reasons. If the point is that your character has grown, then you should probably find a memory or lesson that he's learned fairly recently. That narrows your search, and if it's something that he learned during the narrative, it avoids the sense that you're pulling a solution out of your authorial hat.
The key is making it clear that the outward battle isn't the real problem, the real problem is the character's inner struggle. Both in the story and for you as an author
That'll really dispel any "paper tiger" problems.