Himiko's Palace Escape
Explanation
Normally, to leave the courtyard of Himiko's Palace, one must pass by the guards at the front entrance. During the Evil Rao chase sequence, Issun will prevent Ammy from leaving this way, making it seemingly impossible to leave the palace. However, we can clear the high invisible walls surrounding the palace by jumping onto the slippery collision of the roofs above the treasure rooms and the paths toward them. From there, one can jump or perform a Sliding Ground Tackle to jump over the walls.
This is used in NG All Brushes and Top Dog to more quickly reach the Sei-an Aristocratic Mermaid Spring after talking to Queen Himiko as well as after obtaining Deluge. It saves roughly 8s compared to going through the guards. This is also done in NG+ AB to go to the Imperial Palace dungeon in the middle of the Evil Rao sequence.
Demonstration: https://youtu.be/f5ajRgkdipg
Old Strat
In NG+ All Brushes you used to jump out using three KT Jumps to get over the wall and land inside the walls of the building closest to the Imperial Palace. This was quite difficult because of some weird cursed zone interaction causing a lot of white flashes to occur making it hard to see if you got the KT or not.