The camera is VERY IMPORTANT for this strat, replicate it closely
The c-right input can be either mashed or timed once before entering the door
The dive to the star is not essential and can be dropped for minimal timeloss and higher consistency
Adjust to the left during the double jump to give yourself more space to triple jump if needed.
Back up with Watch For Rolling Rocks if something goes wrong
For ideal door touch you must strain right to avoid the wall, getting a dusty third long jump makes it easier
Alternative Movement
This strat is optimally faster than left side, but its less-scripted nature means it tends to be slower and may be less consistent for you in practice.
For the wall kick, hold up-right and do a buffered kick into double-jump, and start holding up immediately after the kick to strafe along the wall towards the platform. You can also run forwards a bit after entering the room to get the wall kick closer to the platform.
Expert
If Mario slides forward instead of rolling out, you were too far forward and must jump lower and delay your dive more.