Haven't played this yet.
Okay, I downloaded the level and played* up to the part I think you're talking about.
Is it this room?
(http://i45.tinypic.com/259zibb.png)
That jump is possible with the items you have.
(http://i50.tinypic.com/29xj7o0.png)
Get onto the little extension as shown in the image (red jump), then let yourself slide down a little before jumping left and double jumping up (blue jump). Don't worry, there's plenty of room for error as long as you don't rush the midair jump.
Let yourself fall a little bit after hitting your head on the ceiling before making the midair jump, and let yourself continue going left a little afterward before going right. If you try making the double jump too soon, or if you slam the right arrow key as soon as you make the double jump, you'll never hit the ledge in the right way to start climbing.
*Well, I played up to Chapter 3 then decided to skip to where you were in Chapter 4 so I could help you
PS: Unless it's for another room, you should delete the other topic (the button is right above your post) (EDIT: augh, somebody posted in it now. I guess you'll have to leave it there). Whether intentional or by accident, duplicate topics always make a bad impression. :)