*Request so short cheat*
Towards the end of 3-1, you'll find a few blocks that lead a path to a pipe. Get a Penguin suit and run towards the blocks and then press down. Slide and smash the blocks and go into the pipe.
In the area the pipe leads you to, a pipe will release penguins. Just a little below is a space with the last Star Coin. Stand a little to the left where you have a little jump room. The penguins will hit the wall and turn towards you. When one gets near, jump and freeze it, then jump on it.
Just before the penguin will go through the tight space, hold down the down button on the control pad. When you get through the space, jump just before the penguin falls down into the hole.
*You're still holding the down button*
You should get the Star Coin and jump onto a blue line of ground. You just go back into the pipe you entered from and finish the level.