I will start by saying that yeah, this is blatant cheating and basically half a step away from just using SAM, but maybe someone wanna do it this way or maybe you are just curious about glitch.
With that out of the way, I will describe how to get speedrun achievement using this glitch.

This glitch actually doesn't work in the latest version of the game, so you have to get earlier one. And steam actually has hidden functionality to do it.
Open Steam Console (press WIN+R and type "steam://open/console") and type command:
download_depot 499180 499181 7379829663218668436
Where 499180 and 499181 are basically game IDs for Braid AE and 7379829663218668436 is ID of version we need.
Steam will start downloading game, but you won't see any progress bar, you just have to wait for message that it is finished downloading and console will tell where it is saved now.

Copy/move downloaded folder to ./steam/steamapps/common, rename original folder of the game to something else and name one you just moved "Braid Anniversary Edition". Now you can launch the game.

I assume you already completed normal walkthrough of the game. First you have to enter commentary hub, there you have to enter Design door and then Casey door.

After entering Casey door run to the right for five screens until you reach one with three doors on it. You need to enter upper left door.










There you should just press ESC and start Full Speedrun in the menu. When Speedrun starts you should see Commentary doors on starting bridge, it means that glitch worked.

Now you have to run through world 2 ignoring all puzzle pieces. And when you reach hub of world 3, you will see door with arrow on it.

This door leads directly to Epilogue. There you can just run to the right until final door and when you enter it

The end