hehe, I remember playing this game back in the day, and spending literally days trying to figure out how to get past these worlds (I was only 6, mind you). And now we have the luxury of the internet where you can easily ask for help, or look it up with a click of a button. *sigh*
Anyway, I believe what you are looking for are keys and keyholes to make it through the forest. Look for them to unlock the path to progress through. I know theres one in the first level of the forest area, which involve a balloon to help you there. There's also one in the water level of the forest. Also to let you know, if a level (on the map screen) is red, it means that there are multiple paths that take you to different places if you can find the secret way to finish the level. If it is yellow, then there is only one way. Sorry I couldn't be more specific in helping you get through the forest area, but I'm going by 15 years of since I last played this awesome game.