Believe me, it's like I say. Let's resume:
1) You begin on the right side until you reach the room with the key inside. There was one of the platforms probably fallen into the water.
2) You go back and jump to the ledge above the entrance which allows you to shimmy over to the other (the left) side.
3) Now you've arrived on the left side, facing the wall. So please just try the following even if you don't believe me:
a) Turn 180 degree (now facing the other end where you see the goodie you're heading for) and jump to the next platform.
b) Turn 180 degree again so you're facing the wall.
c) Now let you drop down to the platform below you.
d) Next, still facing the wall, jump two platforms so you're at the wall again.
e) From there you can whip over to the lower platforms on the right side.
From there you can continue. Believe me, this is the only way it worx.