Although Juice World is currently far from finished, I have devised/accumulated a few strategies that can help complete the "fastest" run of the game- from the beginning of the game to the completion of the Creator boss fight- in the game's current version (0.0.5 Alpha). As I see it, a fast run of the game currently revolves around the acquisition and use of the extremely powerful Draginslayer sword, which is placed in the mouth of the yellow giant statue (situated directly west of the graveyard, if the exit to the graveyard is considered south). This is because said sword can one-shot the Creator (the game's "final" boss as of the current version) which would otherwise take several clumsy shots with the next most powerful weapon, the ranged Pineapple gun, assuming that you do not run out of energy and get clobbered by all of the Polywogs the Creator spawns . However, it seems that much less leveling is required to acquire the Draginslayer and get the associated level-ups to use it in the boss fight then it would be to have an appropriate level of preparation to fight the Creator with the Ordinary Pineapple.
A few notes for the initial segment at the Juice School:
-Mrs. Slithers' lesson can be skipped by jumping out of the window, and as it is closest, the classroom's middle window should be used. It is also possible to fly to the roof from said window by holding the Space bar upon jumping out, rather than flopping to the ground and then having to zoom up.
-It is also possible to avoid having to interact with Ingot at all, which saves some time - just keep a reasonable distance from him and he won't engage you in a conversation.
-Once you have the mace from the roof, you should use it to smash around 7-8 boxes in order to get the 100 required points of Juice to open the gate out of the schoolyard. At present, I first destroy the three stacked boxes closest to the schoolhouse and then fly towards the stacks of 2 and 3 boxes to the left of the mouth-gate, which gives around 120 juice- enough to open the door.
-Upon falling out of the school-sphere, the logo for Juice world will spin in and hold the character in a free-fall until you skip using the "Q" key (the default key for the Windows version of the game). The title will become skippable at the moment that the title text becomes upright and horizontally aligned on the screen. You should aim to time your q-press to occur as soon as the text reaches that horizontal position.
Notes for the overworld portion:
-You will not have control over your character until you hit the ground, so you don't have to worry about doing anything until then. Once you do, you should attempt to fly over towards the section of the graveyard with the cross graves and the Rune Blade in order to pick up the latter. You will use this to destroy all the headstones on the opposite side of the graveyard in order to summon the entombed skeletons to farm for Juice. Although the shovel is closer to the graves, I find that the sword saves time in dispatching the skeletons due to a greater surface area that the game considers as a weapon, and thus leading to more hits on the skeletons as you flail around. You should also destroy the tree and the attached Koalath for their juice.
-Although Mr. Fox is also a potential source of Juice in the graveyard, I tend not to attack him, as it isn't strictly necessary in order to get enough juice to level up and fly to the Draginslayer sword. However, you may find this a faster method of obtaining juice than destroying all of the graves, and that may be a better strategy in the end.
-AVOID SPAWNING THE VAMPIRE BAT! Though they are charming, we don't have time for their diatribe, nor much use for their vampirism powerup given that we'll be using the Draginslayer, which causes enemies to hemorrhage juice anyways and is extremely powerful. To prevent the bat from visiting, never allow your total amount of Juice to equal or exceed 300 while in the overworld- spend it at the Juice Fountain before then. I find that you'll need to take a break or two from fighting to spend your juice while smashing all of the graves to prevent their arrival.
-Don't forget that the fountain completely refills your health and energy, so you should always spend the energy to fly towards the fountain rather than waddling.
-Level up Maximum Energy, Energy Regeneration, and Flight first, as this is what you'll need to be able to fly up to the giant's mouth to reach the Draginslayer sword, as well as increasing the speed of your flight to make traversal much faster. I tend to spend 180 points of juice each on Max Energy and Energy Regeneration, and around 300 points of Juice on Flight. Any extra juice gets put into leveling up Max Health, due to all the enemies you literally must run into in the Evil Caves (not least of which being the boss).
-As soon as you've destroyed all the graves and spent all of your Juice, drop the sword and fly west (that's in the direction that the graves you just destroyed in the graveyard were in) at a 30-ish degree angle, and aim for the giant yellow mouth of the Fog Giant that emerges from the purple haze. You will not have enough energy to fly continuously, but if you stop flying briefly by letting go of spacebar you can regain enough energy to continue moving upwards. You'll have to use this method of "pulsing" the spacebar while you fly over the overworld and as you navigate the underground tunnels.
-The Draginslayer sword will be laying in the mouth of the yellow giant. Pick it up and start flying towards the skull displayed on your compass in the upper right-hand corner of the screen, pulsing the spacebar so that you never have to hit the ground. It's also advisable to reduce your altitude while making your way to the abandoned cabin so that you won't have to waste any time free-falling.
-Avoid going too close to any trees or enemies, as accidentally hitting anything will almost certainly give you more than 300 Juice. If you do end up doing this, though, you can still avoid the vampire bat if you manage to get into the evil cave fast enough. You can also out-run any accidentally acquired juice by flying in a straight line away from it.
-Once you arrive at the cabin, head straight to the trapdoor and open it. If you have enough skill to fly through the windows rather than wasting time awkwardly ambling through the front door, then go for it! Just be warned that clipping anything with the gigantic Draginslayer will probably lead to you being catapulted out of the room or getting separated from your sword.
Notes for the Evil Cave portion:
-I usually choose to avoid directly fighting the skeleton horde in the basement and attempt to fly through/past them. This is because deliberate combat is far inferior time-wise to just brushing the skeletons with the blade of the Draginslayer to get some Juice.
-Try to avoid flying into the walls of the tunnel leading into the cave as much as possible. However, if you can dangle the Draginslayer into the mob of Dragins at the exit of the tunnel and slay a few of them, then go for it.
-Head towards the Juice Fountain to recover your energy and spend any juice you have on upgrading Flight. There is a high chance that a mass of juice will be tailing you from the fight with the skeletons/Dragins, and although I tend to wait a few seconds to let it catch up, it is likely a time waste. Instead, fly to the hole in the ground underneath the fountain to the entrance and enter the Creator's ethereal plane.
-The fight with the Creator will be quite brief. The battle strategy that I find the fastest is to fly towards him at maximum velocity and hope that the Draginslayer hits him as you slam face-first into his body. This tactic can be risky due to how low your health will be, but it is the fastest method so far.
-Even though the creator is "Dead," he will keep talking to you. You'll know you've won once the Juice Portal exiting the plane appears. Time ends once you pass through the Juice portal and return to the graveyard. Don't forget to activate the portal by pressing the "E" key!
That's about all I have to say. My current time using this strategy on a not very serious run was around 5 minutes and 20 seconds, starting from the point I clicked "new game" on the menu to the point I re-emerged in graveyard after the Creator boss fight. Improvements on execution could probably bring the time down by a minute or so. For anyone who is bored with the game, speedrunning can be a fun added challenge to spice the gameplay up. I look forward to the comments you have about routing, your speedrun times, or alternate non-Draginslayer routes that you might have!