If you're stuck, you're probably not doing it right.

Try different methods.

Go everywhere. :D

If you're trying to do the same thing again and again, and it's continuosly failing, you're probably doing it wrong.

• Try changing the speed (faster/slower movement). Sometimes it's better to go carefully and precisely control, or sometimes it's better to rush.
  
• If it involves aerial movement/jumps, figure out the best shape in the air. Sometimes it's better to be smaller, or sometimes longer.
  
• Look around you for things in the environment that might help you (ex, a rolling ball). For some puzzles, the camera is positioned to show you what resources you need to use.

The main trick for this one is to cut yourself up into many small pieces once you're in the air/when you're separated from the cart. Then, only one piece of you has to land in the cart for you to be able to continue.

Most DNA is out in the open, but there are some hidden pieces that can be hard to find if you're not looking for them. Findng most of these involves going a bit higher than you thought you could. Look for small ledges that you can climb on to get higher. Also, make sure to get all DNA from boss fights.

Find strands by trying to reach places that look like are impossible to get to. The path to some strands involves interacting with things that look like a backdrop.

To control a rocket/make it go one way or another is pretty simple. You have to extend your mushroom down the side of the rocket that you want to go.
Form a little upside-down "u" hat for the rocket. Then extend one side of the hat deeper, and the rocket will move in that direction.
If a rocket is on its side, ride on top of it. Moving to the back end will make it turn up more and allow you to go farther.