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Publication Order is

1) Barkley Shut Up and Jam Gaiden 1 (Tales of Game's Studios Presents Chef Boyardee's Barkley, Shut Up and Jam: Gaiden, Chapter 1 of the Hoopz Barkley SaGa.) 

2) Barkley Shut Up and Jam Gaiden 3(Shitpost edition) (The Lost SaGa) 

3) Barkley Shut Up and Jam Gaiden 2 (The Magical Realms of Tír na nÓg: Escape from Necron 7 - Revenge of Cuchulainn: The Official Game of the Movie - Chapter 2 of the Hoopz Barkley SaGa: Janky Demo Ver) 

4) Barkley Shut Up and Jam Gaiden 4 (Barkley Gaiden²: The Son Of Dark Draker: Barkley Shut Up and Jam: Gaiden, Gaiden Episode 1)

For fans of chronological order, however, switch games 2 and 3.

BABA IS SUIT

Thanks for the kind words!

For New Game Plus, when you start a New Game, press the Plus key.

Good to know! Thanks for testing it

This is a fun game, nice elaboration on the core mechanics and a good short and sweet buildup of how they're used.  

Once you have the hookshot you can go north past the brain bots and get the chip.