The entrance to the forest is filled with chuchus. Kill them, and open the chest to grab the dungeon map. Now pick up the big acorn to the west. Throw it at the flower on the door when its petals are open. Go through the door.
You can just shoot across this room if you want, using the baba buds and the deku leaf. But there's treasure to be had, so drop down to the very bottom, deploying the deku leaf just before impact. There's a treasure chest blocked by a flower. Either pick up a stick from one of the boko babas down here, or use the GBA to have Tingle set off a Tingle bomb on the flower. Open the chest to get a knight's crest. Now use the baba buds and the deku leaf to continue up and up to the next door. Don't stop here. Continue up until you find a joy pendant. Now return to the door and use the bomb flower to clear the vines.
Use the deku leaf to blow the propeller in the next room, which will bring the gondola to you. Board the gondola, and use the leaf to move the gondola forward by waving the leaf away from where you want the gondola go. The next room is full of peahats and boko babas. To kill the former, use the deku leaf to knock them down, then attack. One of the boko babas will turn into a baba bud after you kill it. Use the bud to shoot yourself up to the next level. Attack the next boko baba, which will also turn into a baba bud, and fire yourself up to the gondola platform. Fan the propeller with the deku leaf, then board the gondola. Move yourself across the room, then attack the boards. Grab the acorn and jump on the gondola. Drop the acorn, then quickly fan yourself to the other side. Throw the acorn at the vines and open the door.
The acorn in the next room is blocked by impassable, spiky tentacles that shoot out of the floor as you approach. Use the deku leaf to blow the acorn to a safe spot, then grab it and use it on the door. The next area is huge, but the lower level is not important yet. Walk to the right and use the grappling hook to swing to a platform, then jump to the moving tendrils, finally landing near a locked door. Jump to the moving room in the center of this chamber to grab some loot, then jump back to the locked door and grab the acorn. Jump back to the ledge around the room, and then to the platform with the vine-blocked door. Use the acorn to clear the vines. Note that you can jump to the moving tendril to your left and ride it up to a warp pot.