Roll to the side of the skulltula. You can normally grab the ledge and pull yourself up, but you can add a jumpslash at the end to save time.
Go to the area that would be your path back from Ook. Get on the edge of near the first rotating platform and cue Midna (and exit out of her text box) to switch the wind and have the bridge turn. As it is turning towards you, walk forward to clip into the bridge's railing. Cue Midna to turn the bridge again, jump forward and use a jumpslash to land on the second bridge. You should have a clear path to the area of land with the fifth monkey.
Note: Although standing at the left, right, or middle of the platform before the first rotating bridge will work for clipping, the timing for standing in the middle is the most forgiving.
For the second pair of rotating bridges, head to the edge of the first bridge, position yourself towards the right corner at a 45 degree angle and wait for the wind to turn. Just after the first railing of the bridge passes you, jump to clip into the second bridge. A well timed sidehop will also work for this.
Climb on to the ledge next to the stairs, and line yourself up with the the fencepole between you and the ledge past the fence. Roll forward, and continue holding forward. Link should roll off the pole and directly on to the ledge.
Using the Gale Boomerang, Long Jump Attack over to the monkey tree. Climb the left side of the tree using jump slashes, and then use another Long Jump Attack to jump to the door. Please note there are various different ways to target to LJA to boss door