How do get to this gem behind a narrow passage in Palm Tree Paradise?

In the first level of a Emerald Passage, Palm Tree Paradise, there's a gem hidden in a room that I can't quite figured out how to reach, pictured below.

I've tried everything I can think of to get through that narrow passage but it's just not working. I've bumped around the room thinking there might be some other hidden passage, but there isn't. I tried coming back after the hitting frog switch thinking something may have changed, but alas, nothing did.

At this point I can only assume there must be some move I'm not aware of, or I need to be extremely precise with the angle I jump at the passage.

How can I gain access to this gem?

Solution 1:

So turns out that if you crawl off a ledge you'll maintain your crouching position, and will be able to fall sideways into the passage, as demonstrated in this video: