You must be in the first part all the time.
You must buy the air-floating upgrade and do everything possible to quickly obtain 5 million gold. Meanwhile, to avoid falling into the hole, you can stay on top of the green pipe.
Then, you must place the hole on the wall opposite the concrete structure, half in one square and half in the next.
At that moment, you must jump into the hole and float (just like you got the seventh black star) so that you can jump into the hole, float, and cross to the other side.
You must repeat this three times until you reach the star door.