There is a speed bug in the entrances to the Day & Night towers. (If you know the Yume Nikki desktop chair + bicycle speed bug, it's similar to that.)
This can be accessed via entering the Toy World at normal size, and going up the stairs, to go to the two entrances to the Day & Night towers. With the sliding areas, go at the front of one of the doors, then go down, in such a way that pressing the Up button would lead you exactly at the doorway.
If you hold the Up button, while you are skidding, you will go through the doorway, and enter the Day and Night towers with a speed increase. Equip this with the Eyeball Bomb effect so that you can go to other places as well.
Some acts cancel the speed boost, like climbing up a ladder, or even changing effects, so use wisely.