The hint I can give you is:
1) From the platforms on the right side (where you found the key) you must change to the other (the left) side. There is a ledge just above the entrance which allows you to shimmy over.
2) From there (the left side), try to reach the lower platform at the entrance wall. Once you are there, you can whip over to the right side's lower platforms.
3) Try to reach the last lower platform on the right side, from there you can jump over to the left side again.
I hope I didn't tell you too much.