Swamp, Skull, and Ice Palaces: Vanilla, Vanilla, BOMB JUMP!

My runs through the Swamp and Skull palace were largely vanilla. At this point, I'm not super familiar with any massive time savers that can be done in the Swamp Palace beyond just knowing your route and being able to run it quickly. Skull Palace is a breeze, you just need to acquire the master key for the dungeon, bounce over to get the fire rod from the big chest, then proceed to the final leg of the Palace and the boss fight. There is a neat skip that can be done to get at the fire rod while skipping a few rooms and the act of blowing up the wall behind the chest. 

You can utilize the bomb jump technique to blast over one of the holes and get instant access to the big chest. I failed to try it this time through, but you can see a video of it being done HERE (AGDQ 2013, LoZ: aLttp Speed Run by Cyghfer). This video was actually one of the first speed runs of this game that inspired me to dive into the mechanics myself. Most speed running is done on the Japanese version of the game, and on version 1.0 to boot. The text boxes pass faster in the JP version, and there are a few "features" that were later removed such as item dashing. 

The Ice Palace is probably one of the most obnoxious dungeons in the Dark World. Largely due to the fact that you run through the entire thing to get the master key and the blue tunic, then you basically rerun the entire dungeon to hit one switch and drop back into the correct side of a room so you can advance to the boss room. The skip in this dungeon is a huge time saver, and the bomb jump isn't ridiculous to do either.

The room pictured below is just south of a long moving floor room with a switch in it. Leave the switch so that the orange blocks are in your way in the room pictured. Set up for the jump is roughly pictured below. If you are positioned just right, you will get kicked past the orange blocks and land safely on the walk way (VIDEO HERE, courtesy LTTP4HTTP). You miss out on the armor this way, but the blue blocks are now in the correct position for the hole you need to fall down to later on to head to the boss room.

For the small price of blowing off your face, you can skip half the dungeon

Not sure if it is the fastest method, but as soon as you drop into the boss room you can blast the boss with the Bombos spell if you have it. This will immediately break the ice around him and you can lay waste to the clouds he splits into with the fire rod. If you are not doing a 100% speed run, you will have to rely on the fire rod to melt the ice in which case you will largely be fighting the cloud form of the boss with your sword.

Two more dungeons, then some sweet end game.