1. First Purple Coin
Continue up until you make your way to the single platform in the middle in order to get the key. After that make your way to the highest platform that has a row of bricks on top. Jump underneath the brick in the middle to get the first Purple Coin.
After that, exit to the Green Door at the bottom.
2. Second Purple Coin
Upon exiting the Green Door, move forward on the right most edge of the area to get the second Purple Coin.
3. Third Purple Coin
After getting the second Purple Coin, hop on the Springboard that will lead you to the upper platforms. Walk through the right most area to get on the springboard the left most area to get the third Purple Coin.
To get the key, use the Back Dash Buttons and then jump on the brick on the right to get the key. After that, enter the Green Door at the bottom.
4. Fourth Purple Coin
Upon exiting the Green Door, get the fourth Purple Coin that’s sitting right on top of the green door in the middle.
5. Fifth Purple Coin
Get the key first by moving up and then using the Dash Back button in order to jump on the Boo coming from the left.
Once you have the key, use the Dash Back button once again to jump on another Boo flying from the left.