When you find and complete a Hidden Path a message will come on the screen that says "You Found a Hidden Path" in a blue box.
Level 1-2 (credit goes to UraMallas)
After the second checkpoint you'll turn left and immediately come upon reqular ball switch and some checkered cloth in front of you. Switch back to the regular ball and jump on the cloth to get to the other side. Stay under the cloth and turn the camera so that it is perpendicular to the cloth and you should be able to see two metal bars below the platform. Be very careful and position yourself to jump on the bars so that it will catch you. Stay on the bars until the end (camera is a bit wonky under here) and then jump onto the wood from there jump back onto the normal path and you should get a blue screen that says "You have found a hidden path."
Level 1-4 (credit goes to pavementpoop)
After the third checkpoint you'll come to a gap with two boards over it. Go across the gap and change into the metal ball and go back thto the gap staying in the center of the path. You'll see that the boards look a little different on your side of the gap, carefully navigate onto the boards and you will fall directly onto two metal bars. You'll fall through the boards on the edge not through the two boards over the gap so be prepared for it. From there, follow the path under the boards to get this Hidden Path.
Level 3-2 (credit goes to J2ouai)
After heading down the first set of tubeslides right at the beginning of the level, you will come across an area that has two seemingly useless magnets on each side; both having power buttons you can switch them off with. The area also has crates you climb with the help of a hanging magnet. Turn off the magnets and head up with the magnet. Up on the platform, transform into the metal ball and push one of the metal crates to create an opening. Then head back down to the magnets and transform into the power ball again, grab the magnet ability and go back up and past the metal crate you just pushed. Continue onwards past the cloth, suck yourself toward the magnet and launch yourself out of the cannon onto the floating magnet to the left. Use the second cannon to launch yourself onto the next magnet.
Level 3-3 (credit goes to J2ouai)
When you reach the cannons, fire them as normal and take the path to the power ball and grab the magnet ability. Head back to the cannons and fire yourself out of the first one onto the platform where the second one is. Then fire yourself straight ahead, aiming as far up as the cannon will go, and hold A once you fire. You should magnetize and stick to a big magnet close to the exit.
Level 4-3 (credit goes to atomicsuperman)
As you exit the tube onto steel rails just prior to the rotating hammers, wait for a platform to appear in the distance under you. Fall onto it (use the edge of the tube lip to help you get off of the rails).
Ride this elevator and it will float high up until you can fall into a second tube. Ride this tube under all rotating hammers and you will come out at a cannon. At this point you are back onto the main path level. Two cannon shots and you are at the exit.