I'll try not to give too much away here, but I'll say that what finally hit me was that getting the star on 9,14 taught me something about how the spikes behave. But it took me a long time to realize that it had also taught me something else related that I didn't catch onto at first, which once I realized it was the obvious-in-hindsight key to gaining some extra mobility getting into the "secret" path.
Which kitten are you missing? I might remember how to get it.