Flying is the best way to do this level, Blue Yoshi is extremely helpful. Using a combination of blue Yoshi and caped Mario makes it possible to do this level in two flights.
Ignore the first three Koopas in the level and move forward. You will see a lone green Koopa, let him walk as far to the right as he goes, then eat him to gain wings on blue Yoshi. If you timed this right, just as the wings wear off you will be at the point where a pipe from the ceiling and one from the ground almost meet. You can glide through these, assuming you are caped Mario, onto the platform at the save point.
Use the springboard to get the save point and jump onto the top platform on the right. There's two green Koopas, use Yoshi to eat one and gain wings. You can now safely fly above the enemies to the end of the level. Your blue Yoshi's wings should wear off just as you come to the platform with the end goal on it. Making this one of the easiest levels in the game.