Enter the cave on the left side. Move up to the edge and have the other Links close to you.
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On the GBA screen with the chest that contains the Medallion, select one Link and walk off the ledge, towards the chest. When in midair, press R to roll and then mash A to open the chest (or do a precise A input if you feel like it).
Video
Killing all cyclops and getting through the GBA section can be completely skipped by using GBA OoB. Enter the cave in C-Right formation and perform GBA OoB. Exit, switch to purple and reunite. To be safe, separate the Links again and then walk against the diagonal to perform the Super Jump. Simply walk up afterwards.
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Once you get to the last fire you must extinguish, you need to stand about throwing distance away from the fire before you throw the last water jug to make sure enough fire is gone so you can pass through. Standing too close causes not enough fire to be extinguished.
On the second screen, you can skip a short part by Freeze Clipping through a wall. In combination with taking additional water pots, this results in the old water pot method to extinguish all fires without the need of refill. To do so:
Note: The video differs from this description, but shows the basic idea.
Video
To enter the cave where the Firepots are stored, you typically need to hit the pegs outside using the Hammer. However, by doing a spin attack while in a C-Left formation right next to them, you can somewhat clip into the ledge, forcing Green Link to jump down. You still need* a Hammer for the boss fight, but both GBA screens there have one.
*Note: You can actually damage Helmaroc's Mask with Bombs too, but from a Speedrunner's perspective, using the bombs on the TV screen takes too long, or even getting Bombs on A.
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By using FLG with an item you can access the transition early by going over the warp actor on one of the two cave entrances near the top of the screen. Simply get FLG, walk "into" the cave and throw the item. (If you have low enough FLG, you can transition without letting go of the item).
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During Helmorac King's second phase, you can deal enough damage to defeat him without the need of a second bomb. This seems to be very precise and is usually easier if he falls near a wall so you can jumpslash in the same direction each time.
Obsoleted Tricks
Note: This belongs to an ancient route and is no longer relevant in its form.
Using water jugs wisely, one can skip a key later in the level that normally is needed to obtain other water jugs. To do this, when going to the screen with the first dark link go into the first cave right in front of you. Grab three water jugs from this room and follow the video on the usage of them.
On the floor with the maze of flame jets and the boomerangs just to the right of the entrance from the previous floor, it is possible to roll past the flame jets. To do so, get into a C-right formation, roll right, and immediately press X. Purple should dim in the middle of the rolling animation and just make it past the flame jet. From here you can grab a boomerang and proceed.
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When you enter 3F, do not step on the moving platform, but walk to the right edge instead. Perform a Wall-less Gap Skip, switch to Purple and enter the next floor.
You want to position Green below or above the gap that surrounds the key door, then place a Link on the other side. Switch to Green and reunite so all other Links will float towards him. When the desired Link crossed the first gap, press X to interrupt the reuniting effect.
Obsoleted Tricks
(You need Roc's feather to do this)
Entering the screen before the Shadow Link Fightt, you can quickly switch to Red and jump throw Blue to the platform moving away from you. Then you can quickly switch to him and jump over to the second platform, ultimately getting to the exit of the room one cycle earlier.
Note: It is suggested to enter this screen using green. This is because entering with a different Link will cause them to get called on top of one another, making this early cycle very difficult to do.