Pillar Clip can be done without Zora Armor or the Air Replenish Trick by sinking to the bottom of Lake Hylia before warping the meteor to raise the water level, and it requires Early Master Sword. From here, Link can use the pillar to clip through the wall, and can barely reach the Lakebed Temple loading zone without running out of air.
The following video shows the old school setupless method, which does not call Midna prior to the clip. This method is one of the hardest ways to perform Pillar Clip and has since been obsoleted by modern techniques.
It is possible to perform Pillar clip with high water in Lake Hylia using the cucco cutscene to pause the air meter. However, as this requires already having the clawshot, it is usually better to return to Lakebed Temple with Ooccoo.
A rupee dive can only be done with rupee text (blue rupee or higher value). The quickest way to spawn one is to dig up a patch of dirt close to the dive spot, but one will not always appear.
The timing for step 3 is difficult. If Link swings the sword too soon, he'll get the rupee in midair and the animation will not happen, preventing him from diving out of bounds. However, this is easier than standing on the very edge, not swinging the sword, and hoping the dive works.
A dive from Lake Hylia with low water is also possible using a pot from Fyer's hut. This isn't faster, but it is easier and also makes it possible to get into Lakebed earlier.
After knocking the Boss Bug into the water, it is possible to call Midna on the same frame the Boss Bug disappears to Midna Dive. It is then possible to swim up into the Lakebed loading zone.
Using Ooccoo at the edge of the planks in the water, it is possible to dive down under the floor collision.