Peet can do more than just that lame bounce hop of a jump and standard walking using his 'special' moveset.

Umbrella Boost (Skateboard)

• Pull out your skateboard *Moving or still, does not matter
  
• Jump
  
• Hold a direction left or right + Jump again to pull out the umbrella
  
• Land on your skateboard to maintain your speed

***You must be on 'flat' ground, a type of surface that the board can be used on. This includes but is not limited to, surfaces that do not have any grass/plants growing on it (one exception would be in the sewer boss fight), wooden crates, concrete blocks, stairs and anything with a curved surface clearly meant for a skateboard


Umbrella Boost (Bomb)

• Grab onto a bomb *Always grab the opposite direction of the bomb that you intend to go, this allows for you to get the momentum off the first swing instead of having to swing twice
  
• Swing the bomb back and forth to gain momentum
  
• Release from the bomb while on the outer limits of the swing and immediately open your umbrella

***If you are chaining a bomb boost into another bomb (Tarzan?) you want to hit the biggest bomb always and its pretty much an immediate release or you will lose all your speed


High Jump

• Jump
  
• Open your umbrella at the peak of your jump
  
• Hold up and swing your bat

***Can also be used as a wall climb if you do it against a wall or an improved high jump if you do it while being flung up a levered platform, can also be used to gain height/distance during an umbrella boost

Moon Jump

• Have Peet walk back and forth on the very outer edge of a levered platform, the best way to explain it is pretend like youre trying to get as close to the edge without falling off over and over again

***This only works on the moving platforms with a lever on them far as I can tell, at the time of writing this ive only done it using the cemetery platforms

Mountain Climber

• Jump
  
• Pull out your umbrella
  
• Hold the direction of the block or object
  
• Swing your bat like you are attacking the block or object

***To be used against concrete blocks and other surfaces that can be hit, you are able to 'climb' some vertical surfaces.

Gravity Stomp

• Jumping on platforms that move pushes them down slightly

***Only saves a very small amount of time, not worth it unless you are doing a speedrun

• C G C G B
  
• B C D A E
  
• B B D E A
  
• A G F E D
  
  
• D C D E A

The first four are your gear and the last one is to be played once you beat the final boss.

• Play the four songs to obtain all your gear
  
• Head EAST towards Neverwood Cemetery
  
• Speak to Simeon
  
• Speak to Gomgirlssa
  
• Get Nails
  
• Speak to Gomgirlssa again
  
• Smash 3 grown up cages
  
• Beat Mr. Toyne and grab his song
  
• Grab the Needle in the tree
  
• Pop Simeon and enter Spidarian Sewers
  
• Roll Simeon through dirt, sludge and eggs and up to Mrs. Richardsons mouth
  
• Beat Mrs. Richardson and grab her song
  
• Grab the song in Redwind Village located in the last house by the waterfalls
  
• Head WEST into Booty Bum marsh and speak with Preston two times
  
• Grab the gold key inside the water tower
  
• Unlock the Booty Bum hideout and read the book on the table inside
  
• Speak with Soyler twice, the second time say "Collin James Coy" and you must read the mail
  
• Bomb the concrete at the waterfalls to obtain Sugar Blasters
  
• Take the Sugar Blasters to Skunky in Booty Power Co.
  
• Speak with Skunky twice. First time you speak with Skunky you must answer "How so?" and "Please?"
  
• Hit the lever next to the flower pot that pops up
  
• Grab Grannys song
  
• Take the elevator up to Blackfork
  
• Enter the Blackfork Asylum
  
• Enter the door code: Peeter Smile
  
• Beat Dr. Smile, grab your song
  
• Play the final song

https://www.youtube.com/watch?v=vXLDVfoQcu0&ab_channel=Download

https://www.youtube.com/watch?v=zaKmveE1Ftk&list=PLF9h_DY2_owVxdiXglUVOpkyXY8RYVzE_&index=1