Left-side (double-jump) wallkick. After entering the mansion, hold slightly left to turn Mario, but don't hold all the way left until you have jump kicked. If you don't do this, you will be too close to the wall when you double jump and won't get enough height from the wallkick.
An alternative RTA strat that is generally not recommended. To do this more consistently, angle sharply facing the right wall, but strafe left during the jumps to avoid the protruding wall corner.
