All dreams containing a hidden level are listed in order of appearance by their in-game title and a short descriptor. Text and images revealing the location/tasks to enter the hidden levels are behind spoiler formatted text. This guide will not showcase or display these hidden worlds as it only serves to get you there.
This guide may be updated or a new guide may be created in the future to include various easter egg locations and fan art rooms as well.
Sorry if spoilered images behave oddly. Blame Steam!

LocationRock pit next to Sage Bernard
Tasks

• Speak with Sage Bernard (The pit will become lava)
  
• Jump into the newly formed lava pool.

LocationCracked ice wall near fallen billboard
Tasks

• Give Biscuit her favorite red ball
  
• Exit the cave and platform to the nearest building
  
• Walk along the fallen telephone pole to the second building
  
• Do not jump all the way down and instead follow the cliff paths to the side
  
• Continue on until you find a cracked ice wall
  
• Walk into the cracked wall and interact with the object inside

LocationThe open grave in the far left corner of the acid split graveyard
Tasks

• After entering this dream follow the cobblestone path
  
• When met with the acid pool graveyard walk the left edge towards the graves
  
• Continue till you reach the open grave in the corner
  
• Jump into the open grave

LocationThe painting above the Ghost King
Tasks

• After exiting the cellar talk to the Ghost King
  
• Do not collect the shard and instead wait for the painting above the Ghost King to change
  
• Climb up the Ghost King to reach the painting
  
• Jump into the painting

This isn't necessarily a hidden dream but I thought it should be included anyway.

LocationThe end wall of the unassuming hallway
Tasks

• After exiting the elevator turn right and head into the hallway
  
• Walk to the end of the hallway
  
• Walk into the wall