Throw a bomb on the west slide and step on the center platform before it detonates and activates the switch. Throw another bomb to the northeast window to break the wooden panels blocking it. Exit through the north door.
Dash north to the other side of the room, then west until you press the ground switch. Place a bomb on the cracked floor tiles and use the Hookshot in the south direction to grab the Small Key before the bomb explodes. Unlock the north door to reach the next room. (See 1F Quick Small Key Grab)
Go down the stairs to your right and merge the wall just north of where you are. Walk left in the wall until you reach the second small alcove. (While walking in the wall, you will see Link take 2 "turns" in one direction, then 2 in the other, and then 3 other ones in the first direction. You'll know you're in the right spot after that final turn.) Bomb or Hammer the floor at the south end of that alcove and jump down to B1.
Grab the Small Key near the place where you land. Jump down and go through the staircase northwest of your location. (Use the white mask on the wall above the staircase to locate it.)
Take the other staircase to the right of the one you just used to go up to 2F.
Walk a few steps south and dash east to reach the next room.
Use your sword to break the east and north skull surrounding the torch, and to take out the fire as well. Grab the Small Key with the Hookshot. (See Quick Small Key Grab In B1) Make your way along the bridge to reach the southwest door.
Cross the room to get near the west wall. Use the Ice Rod to activate the switch on the level above. (See Early Boss Door Room Switch Activation) Unlock the southwest door to reach the next room.
Throw a bomb down each of the slides to activate all 3 switches. Get the Big Key chest and exit the room the way you came. (See Fast Bombing Method For Big Key)
Throwing 4 bombs directly on Gemesaur's face mask during the first phase will cause it to break. If the bombs hit the mask on the side, they won't do as much damage and more will be required in order for it to break. If you have the Stamina Scroll, it is possible to throw all 4 bombs without having to wait for your energy to refill. If you don't have it, grab one of the Energy Potions from a pot nearby after 3 bombs.
Here's a video of the optimal method for the first phase (with the Energy Scroll):
The second phase is really simple. Hit his head until he takes out the fires, then use diagonal dashes to reach and light up both of them (you won't take damage and he won't stop you while you dash). Finish him up by slashing his head some more. It is possible to complete his second phase in 2 cycles.
1F Quick Small Key Grab
In the second room of the Palace, after pressing the floor switch in the north-west corner, it is possible to grab the key from across the room using the Hookshot. To do so, stand in the circular light and aim south. Also, the tile under that light needs to be destroyed in order to complete one of the Palace's puzzle. A common method is to place a bomb, then use the Hookshot to grab the key before finally making your way to the locked door on the north wall.
Hookshot On 2F Spinning Wall Switches
In the first room of 2F, you are supposed to place bombs near switches, and then merge or stand near a certain part of walls when it detonates to access the other side. By standing near those specific walls, and using the Hookshot to activate the switches from a distance, it is possible to walk towards the wall while it is spinning and get past it. This saves having to wait for the bombs to explode in both cases.
Eyeball Lighting Scene Skip in 2F
Using Success Skipping, it's possible to skip the scene shown after blowing up the windows planks on the eastern wall.
Quick Small Key Grab In B1
In the north-eastern room of B1, it is possible to grab the key lying on the floor in the corner by using the Hookshot. This saves having to walk the path hidden path all the way to it.
Early Boss Door Room Switch Activation
The Ice Rod can be used to drop a bloc and activate an elevated switch on the western wall, which gives access to the Boss Door. This saves getting a small key and having to go out of your way to reach the platform where the switch is placed.
Fast Bombing Method For Big Key
It is possible to throw bombs down the 3 paths all the way from the right side of the low wall, skipping having to take the platform all the way up to the 3rd path, falling into the void to reappear and walking across the whole room to reach the Big Key chest.