Instead of turning off the first two flame jets, simply walk into them and take damage, then quickly roll through them while temporarily invincible. You'll also be fine if you hit the fire at the end of your roll. If you're in the middle of a roll however you will get smashed into the lava.
After passing the second flame jet, you can Long Jump Attack across the lava. Simply take out the Gale Boomerang, target over the giant switch that unlocks the next room and jump across when the boomerang is over the switch.
Quickly roll to the right to land on the platform below and grab the key, then quickly make your way to the rotating platforms. If done fast enough, should be able to make your way across the platforms without having to wait for them.
In the third room of the dungeon, instead of pulling the stone slab out all the way, pull it back three times, then quickly walk around to the right side of the slab and roll into it to clip inside of the slab. Keep rolling forward until your pushed out on the other side of the wall, and make your way to the door.
Grab the underwater key in this room, then swim over to the underwater block. Instead of pushing the block, simply dive under the fench with the iron boots and swim up to clip past it.
You can skip activating the second Magnetic pull by using an LJA over to the crystal switch aiming at the pipe.
You can skip cutting the ropes and dropping the bridge with Long Jump Attack. Walk past the Beamos Statues to the end of the platform. Walk over to the right facing the bridge and position yourself so that the left half of Link is lined up with the small opening. Take out the Gale Boomerang, try to target between the gap, above the door frame, and Long Jump Attack. The speed of the attack will allow you to clip through the tiny gap as long as your sword doesn't bounce off the wall.
In the room before the second key shard, you can Long Jump Attack over to the door leading to the Dangoro fight. Simply run past the first spinning platform, turn right, R-Target over the top of the door frame with the Gale Boomerang and Long Jump Attack.
Alternatively to using the magnet outside you can LJA across without having to activate the Magnet. Instead of using the initial LJA you can also do two jump attacks to get onto the railing, using the wooden block on the left.
The following is a variation on the above method.
You can also use this out of bounds movement to get over to the bridge area. This is around 10 seconds slower than the above method.
When you enter the room, it's easier to shoot the bridge down first so that you can run past the enemies, instead of walking down the path and being forced to kill the archers.