ACK - the infamous "pillar" puzzle on Otoh Gunga. Wow. Would it surprise you to know that a big reason why TPM was panned so much by the critics is because many of them gave up there, and reviewed the game as if they finished it? I've had several reviewers admit as such to me. Ah well.
The solution? DON'T PANIC. Trust your feelings. Let go. You have PLENTY of time to jump to the next pillar once the pillar you're on starts sinking. Make sure you DOUBLE-jump, meaning tap the jump key, and when you reach your max height, tap the jump key again and you'll do a flip that gives you extra distance. Once you get the hang of the double-jump, the puzzle is easy.
1. Jump to pillar.
2. Land on pillar.
3. RELAX. You have plenty of time.
4. Rotate yourself towards the next pillar.
5. Repeat as necessary.
One of the main things that I saw people doing was flailing themselves all over the place trying to jump IMMEDIATELY when they landed. Stay calm, focused, and you'll make it.