It's possible to reach the switch that unbars the door on the west side of 1F early. This skips all the rooms on the east side of the first floor, including the first Lizalfos battle.
Doing this as an adult is trivial, since adult Link is tall enough to grab onto the ledge with the switch. As a child, you can grab onto the ledge using a Ground Jump
If you have a strength upgrade, such as the Goron Bracelet or Silver Gauntlets, you can simply pick up the bomb flower and store a ground jump off it like you would with any other bomb. See the Ground Jump page for methods.
If you don't have a strength upgrade, you'll need to store a ground jump off a Bombchu explosion, using the bomb flower as your grab-able object. There are three ways you can do this.
It is possible to reach the bomb bag chest starting from the south side of the room, skipping the flame circle rooms and the second Lizalfos fight.
This is generally viewed as the method of choice.
This method doesn't require a shield, so it is useful if you happen to have lost it or are skipping it.
Adult Link can grab the pillar with a simple, well-angled jump. [visual aid to come]
With a bottled fairy, you can do a hookshot megajump to get onto the 2F bridge as soon as you enter the main center room. You need to stand in a position that is below the bridge so that you will land on top of it. The fairy will revive you and you will be free to get the bomb bag quickly. The lava, bombs, or bombchus can be used for this megajump.
Using a series of precise jumps and alignments, it is possible to jump across all of the flame circle platforms without needing to shoot the eye switches to extinguish the flames. The following video shows how to set up each jump.
You can light the dodongo head's eyes with bombchus from the main room, allowing instant access to the end of the dungeon. In most cases it is preferable to go through the dungeon to get the Bomb Bag, but in certain scenarios this could be useful.
Begin by going to the back right corner of the main room at the bottom of the stairs, facing the back wall. Align the right edge of C-Down with the line. Drop one bombchu immediately, and drop the second one at the peak of the second flash.
A more recent setup is seen in the video below.
Using a Staircase Hover you can reach the block in the north room without going around normally. This saves about 10-15 seconds over the normal route.
This hover is not needed as adult, because adult Link is tall enough to simply climb up the ledge to the block.
You need a bottle with a bug or fish to do this trick. Using Ocarina Items allows you to keep the item in the bottle, but can make it more difficult to backflip out of the hole. Using the bottle switch trick costs you the bottled item, but seems to make the backflip out of the hole more consistent.
Ocarina Items method:
Bottle switch trick:
King Dodongo can be defeated without bombs or a strength upgrade. This is mostly for a challenge, and is usually not useful in speedruns.
This trick is used in the current Child Dungeons route to skip bombs. It it used in correlation with lighting the eyes with chus.
Note that this is a very precise trick.