Worlds 4 & 7 - Secret Endings to Open

There's only one way to unlock worlds 4 & 7, and, you guessed right, you have to defeat the bosses petey pirahna and the mummy-caterpillar-thing. The secret is, ground pound them, and it will count as if normal mario had jumped on it. Hope this isn't confusing, and helps!

There are no "other ways", only one. Win as mini mario/luigi
I have no idea who told you about the red flags to get to 4&7
But it is not true

You have to bum bounce and be mini Mario/Luigi to get to the next levels.

Have fun! ;)

THERE IS ANOTHER WAY!!!! If you can at least get to world 4 by beating castle in 2nd world as mini mario...go to the ghost house and you can get a secret exit that will take you to world 7....you will need a mini mushroom though...you will get to an area where you have to highlight the red blocks to go into a green pipe hanging towards right side of screen, there are one of those blow up ghosts in this room.....jump on top the green pipe, turn into mini mario and jump over to the right...you will land on a padding of 3 bricks...follow this up and you can go out secret exit

Beating the W2 boss as mini mario is the only way to get to W4. You can get to W7 by beating the W5 boss an mini mario or by doing this:

Bring a mini mushroom to W4 Ghosthouse and hit the red ! switch that is around star coin 2. Instead of going through the pipe that it leads you to, stand atop it and wall jump to a ledge above in the ledge. There holds a door to W7

i have got to both, world 2 ground pound the mummy thing when it is only 3, world 5 there is a big flower when it tries crushing u move and it falls over, just ground pound it too, u have to do it three times on both (hope it helps)