Metal-Head Mario Can Move! is the third mission of Hazy Maze Cave. The strat to activate the switch from freefall is known as Christmas Miracle.
General strat
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Sideflip backup for missed TJWK. (Alternatively, you can elevator clip.)
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If you fail to activate the switch, get out of the water, double jump backwards, and kick at its peak.
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If you're having a difficult time getting the triple jump correctly, taking the triple jump a bit slower may be a bit easier.
Activating the switch depends entirely on the height of the wall kick, so the most important thing to aim for is wall kicking at the highest point of the triple jump. To do this, follow these tips:
Start with a buffered kick to guarantee minimum kick height.
Do as small a double jump as possible.
Strafe left along the wall between jumps to buy space to fit in the triple jump.
To quickly get out of the water, dive late and close to the far end of the button, then time a swim.
This lag reduction is recommended for players with a decent understanding of the game's camera controls. If this camera setup proves too difficult, spamming C-Right while opening the second door is the next best option.