8-1 (Realm of the Heavens)

Map

8-1 is the first level where there is a fairly significant difference between JP and other versions of the game.
On JP, we make use of jump slashing to reach screen transitions over voids, but on US and PAL, most of these screen transitions don't work (however, a few still do).

Gem Routing

There are two sources of randomness in the gems in this level: the gem rain from the Ball and Chain Soldier, and the Lobster.
The gem rain is guaranteed to give a 100 gem and a random number of 20s and 5s.
The Lobster drops 5 gems that are each either 100 or 150.

Collect:
55 while jumpslashing through screen transitions.
100 and 300 (455 total) from the screen with the beamos.
Lobster and gem rain. Ideally you have at least 1500 after this.
150 and 9x20 (+330) on the screen after the tektites.
If needed, 100 on the elevator screen.
If needed, 100 on the final screen (slash near the bottom below the gem barrier).

If your gem count is very low toward the end of the level, you may need to kill a Dodongo to get either 100 or 150.

Note that on US/PAL, you won't get the first 55 gems since you'll use a different method to bypass the first gap.

Roc's Feather Skip

On JP, simply jumpslash up to the screen transition on the left side of the fire barrier, then back down on the right side. Make sure that your jumpslash is positioned correctly, or else you will end up transitioning over a gap, resulting in a softlock of infinitely falling. If this happens, you will have to exit the level and restart.

On US/PAL, you can use a rolling gap skip.
Start by doing a C-Up formation and standing basically as far up and right as you can.
Move Blue down near the bottom wall, then roll to the right and C-Right formation at the same time, followed by a couple more rightward rolls.
If you don't roll at the same time, Purple will not make it across and will just fall in the void.
Start holding left, and when Green gets back onto land, move him a couple tiles left so that Red and Blue have room to stand beside Green without getting sucked into the void.
After this, start mashing X to prevent Purple from respawning in formation.

Video

Key Skip

There are two possible methods for this, one harder and faster, and one slower and safer.

Formation Hover

The harder method involves a Formation Hover and can only be done on JP.
Start by jumpslashing into the transition above the wall, and start holding C-Right during the transition to start the formation hover on the next screen.
Before reaching the cloud to the right, you must switch to C-Down (recommended to pause buffer this) until the moving platform catches you.
Move onto the static cloud and start another formation hover from there to the right, switching to down before the screen transition to land on the wall.
Finally, you can jumpslash to the right from here to make it to the next screen.

This strat is risky. If you mess it up and fall in the void, you will be stuck in an infinite falling loop and forced to restart the level from the beginning.

Pickup Clip

You can do a simple 1-tile Pickup Clip to get past the wall where the key block is.
After this, you can fight the 3 soldiers normally to advance to the next room.

This is the only method possible on US/PAL.

Video

Colored Bridges

This screen is another routing difference between versions.

On US/PAL, you can only jumpslash to the screen transition on the left, near the wall.
After this, you can pass the next colored bridge without pegasus boots by performing well timed rolls as soon as the colors change.

On JP, you can transition anywhere off a jumpslash.
You can do a small formation hover near the top right of the screen into a jumpslash to skip the longer bridge entirely.
Again, be careful about your positioning with the screen transition, being too far left here will cause an infinite void loop.

Elevator Skip

This is a simple C-Right Formation Hover to reach the switch without using the elevator.
The fire cycles can be annoying, but if you enter this screen at the right Y position and go straight into the hover, it will be timed right to avoid the fire.

After hitting the switch, you will usually have to press X once to fall into the void.

Dodongo Skip

Roll FMC

As Green, start a roll towards the flame wall, then perform consecutive FMCs.

Note: Voiding out Green (for example by throwing them off the clouds), they respawn with invincibility frames for a short moment.
These can be used to make the FMC easier.

Pickup Clip

Alternatively, you can use a 2-tile Pickup Clip next to the bottom statue.
The Dodongos are somewhat random in their movement but ultimately do try to track your position, meaning you may have to lure the one on the right away to be able to do the clip.

If you position the Links halfway over the broken pot tiles before doing the clip, it is possible to avoid taking damage to the fire.
This is useful depending on your gem count, as the fire barriers will make you drop gems when getting hit.

Death Push Clip Method

By pushing a Link into the flames and letting them die there, they respawn inside the flames, and can casually exit the screen.

There are two setups, both are fairly consistent, the second one is slower, but safer.
Detailed explanations can be taken from the descriptions of the linked videos.

Roll Method Video

Hop Method Video

Obsoleted Tricks

Dodongo Skip

Formation Hover Method (JPN Only)

Note: This is an ancient relic of historical value.
On the screen with the Dodongos, do a Formation Hover to the side of the screen, hold C-Up and jump slash.
Doing this correctly, you should have gone to the screen to the right and should be falling.

Now, after the death animation has ended, holding C-Down should result in a wall formation hover. Then, doing a Wall Formation Hover to the right you can then land and switch to Blue.
Then after the second death, Green should be pushed onto the cloud.
Holding C-Left will call all the links and cause you to spawn on the cloud.