Early Thunderstorm (AKA Oni Island Skip, Labyrinth Skip) is a trick which bypasses the exterior and much of floor 1 of Oni Island. This involves getting out-of-bounds and traversing the sides of the volcano to reach the statue of Gekigami, then using Rejuvenation from out-of-bounds to obtain Thunderstorm and be placed back in-bounds.
It is possible to quickly reach the statue via an Origin Warp, performed by jumping on the first frame after entering Oni Island. Then, KT to either side over the invisible walls corresponding to Otohime's fins, and drown in the water. Ammy will respawn far above the center of the volcano, after which you can KT toward Gekigami's statue.
Unfortunately, this trick is frame perfect and cannot be re-attempted, as it isn't possible to quickly leave and re-enter Oni Island. The cost for attempting this trick is extremely low, as you can hold a direction and check whether Ammy makes a footstep sound before jumping, which would indicate that the jump was not frame perfect.
If the Origin Warp method does not succeed, you can simply dash closer toward the volcano and use KT's to get out-of-bounds and onto the side of the volcano. From here, the method is the same as the NG method, described below.
Begin by performing Inferno Pillar Skip to get onto the upper platform that leads into the volcano. Rather than moving forward, dash into the corner to the right of the small staircase. Jump, double jump, and air tackle right to bounce left over the invisible wall. This will place Ammy out-of-bounds next to the staircase. From out-of-bounds, you can simply jump onto the slope of the volcano.
At this point, Ammy will constantly slide down the volcano, but you can maintain and gain height by repeatedly jumping just as Ammy hits the ground to minimize slippage. This is called Greenhopping. It is possible to maintain gold dash through the pillar skip and out-of-bounds jump. If you have gold dash, you will move slightly faster while greenhopping, but will slip down the mountain faster, making the trick more difficult. Depending on your experience Greenhopping, you may prefer to deliberately lose your gold dash during the trick.
Roughly 2/3 of the way around the volcano, there is a large black spot which serves as a reference point for your height relative to what's needed to succeed at the trick. You should be above or right at the top of the dark spot. After this point, it is only needed to maintain height up the mountain as you proceed around it.
When you approach the statue, use inner camera to bring the brush camera closer to the statue before you brush to use Rejuvenation. If you aren't close enough and Rejuvenation doesn't activate (the ink doesn't turn smoky), draw an extra dot after the initial squiggles to avoid them being recognized as Fireburst or Galestorm.
Note that you must get fairly close to the statue, both laterally and vertically, for Rejuvenation to take. If you are too low on the mountain when you reach the statue, it can be difficult to regain the height up the slope needed to get in range. The most reliable and effective way to do this is to ground tackle toward the slope (or slightly off-angle to avoid losing momentum when you jump), jumping and double jumping forward, and air tackling to bounce off the slope. This should cause Ammy to consistently become grounded when she lands on the slope, rather than slipping down. This can be repeated to gain height relatively quickly, as a backup strat if you fail to gain and maintain height while moving around the volcano.