Don't focus on Double Jump only. Focus instead on playing as well as you can with the double jump, and only use it when it is pulling you out of a tough spot when no other option will.

Unlike in other games Gems are a distraction because collecting them will often put you in tight spot and the only thing you can do with them is changing how the game appears. Worry about the gems only when you're just playing a session to goof around.

Keep in mind you'll need to precisely time your leaps in order to get far in the game.

When double jumping, you must also exercise caution. You'll get the most air if you jump again at the peak of the first leap. Otherwise, you're headed for another failure.