Chariot

I found that the level 3-2 was the first and easiest Alternate Exit you encounter.

The door with the red arrow on it is where you need to head to, pretty easily done, you'll end up at the right side of the map shown above through natural level progression, when you get there you need to just take those little islands that head towards the door with red arrow on and your done!

Level 3-2 Entrance A
Any gadget

Follow the level to the right until you're faced with a choice of either continuing right or go down. Go down and you will be met with a blue rail heading left, ride on this until you hit a floating platform, above this are several smaller floating platforms. Get onto those platforms and follow them to the left to find the exit.

Here's a video!