Going through Child Spirit, there is a room with a bridge up, stalfos, and green bubble. There are numerous ways to get across this room without using the boomerang on the switch.
If you have the slingshot, simply open the door to the room and then turn right and back. Get right in the corner of the room without falling off the edge, and you should be able to just shoot around the bridge and hit the switch.
As long as you have a deku shield, you can do a megaflip across the gap off the Stalfos's attack.
Again if you have the Deku Shield, it is possible to use the Green Bubble's attack to hover across the gap as well. This way can be tricky because it is possible to kill the bubble in mid-hover.
If you happen to already have bombs or chus, an explosive can hit the switch through the bridge or by sending a chu around. If you are standing right on the ledge, you can shield drop a chu after the 2nd red flash and it will explode on the switch.
Using a very precise jump and then jumpslash, it is possible for the green bubble to damage you across the gap. This way is extremely difficult and not recommended, but it is possible to do with no items outside of a sword/stick to jumpslash with.
In order to obtain the chu chest as a child, the crystal switch in the room with two lizalfos must be hit. Typically in a run this is done with the slingshot or the boomerang, or else another explosive. However, with very precise hovering, it is possible to use the lizalfos attacks to hover up and hit the switch. This is not a highly recommended trick because the enemy manipulation is very difficult.
The last puzzle in the child side of spirit includes 3 components: Getting the silver rupees to light the torch, lighting all the regular torches to drop the key chest, and pushing the sun block to open the doors. The first part of this puzzle can be skipped. Using the torch from the upper part of the main room, do the flame storage trick. Just before leaving the room to head to the corridor into the puzzle room, pull out your deku stick. If you move quickly, you can light the first torch in the puzzle room before the stick burns out, which resets the timer on the deku stick burning and allows you to light all the torches in the room.
It is possible, using various techniques, to cross the balcony in the main room and gain access to the adult side of the Spirit Temple. If you have a key you can enter the upper part and obtain the mirror shield as a child, or go down to the lower adult side and obtain another key or gold skulltula.
If you have explosives (both bombchus and bombs work), you can start on the child balcony side and hover along the wall to the other side. This can be done in as little as 3 chus if you need to spare them, but requires precise angle and timing.
From the child side, roll off the ledge and jumpslash to land on the hand. Climb up the arm and angle yourself slightly to the right. Roll off the arm and jumpslash. With good timing you will be on top of the shoulder. From here angle yourself again and sidehop into the necklace. You will slide around to the adult side shoulder. From here jump down to the adult hand, and then jump to the ledge. This way does not require any explosives but is quite precise.
If you push an armos across the room, you can do slingshot hovers with chus from its head. It will take about 4 or 5 chus to reach the ledge. This way is not recommended because pushing the armos across the room takes a long time, but it is an option if you are particularly good at slingshot hovering and have the explosives.
If you perform the previous trick, and also have a small key from elsewhere in the temple, you can enter the upper adult side of the Spirit Temple. So long as you have one more explosive to knock out the beamos in the next room, you can navigate all the way to the Iron Knuckles and kill it to get the Mirror Shield as a child.
There is a Gold Skulltula in the adult side of spirit that requires the Song of Time to move a block and receive a token. If you again perform the Adult Side as Child trick listed above, you can head down to this room provided you have a key. Once in the room, as long as you have the boomerang, you can use it to kill and collect the token through the block.