I know of 4 time saves. (sorry I cant post videos)

1st is a minor save in the tutorial puzzle. just run to the wall below the ladder and mash jump. you can get a double/wall jump and reach the ladder. if you get is fast enough (it is easy) you save some time not grabbing the letter to jump off of.

2nd: this one is the hardest skip. and saves about 25 seconds. the puzzle is the one with two snap/ span. the intended way is to drop the ladder down, turn on the snap/ span turn it off when it is open then make the jumps. however, with precise jumps you can just make the jumps without the ladder or turning on the switch. it can actually be one cylced. good time save.

3rd]. know as the escape skip. Found by @MaturedSinner . instead of doing the puzzle you can push the "c" to the left to get to the lower level. push it to the left again and keep following it. during the transition from bottom to top, you can jump and make the hero disappear. the just run to the right until the camera zooms in then pause and retry to warp to the next cutscene. good time save.

4th} I call it the sort skip. it is also realatively easy. It is the numbered puzzle where you make sort/order. to make a bridge to get across the gap. you need to also protect yourself from the gun. I use cover. right before the puzzle there is a small cutscene.

how to skip; right before the cut scene starts, jump forward into the letter maker. you can start to make "cover" during the cut scene. use the cover to get to the floating number blocks. with good jumping you can get to the lower right most block. jump off of it to the right as high as you can. you will die. you will respawn on the higher ledge as if the puzzle was completed.

Platform skip. https://www.youtube.com/watch?feature=youtu.be&v=HyTGOhvRrFs

as far as I know those are the time saving tricks. other than that it is just clean platforming and puzzle solving.

trying to get videos of these.

Tut skip. minor save

Snaps skip

Escape skip (found by @MaturedSinner )

Sort Skip

splitting hairs here but you can save a tiny amount of time in the very beginning. as just the "O" when you fall. if you hit back right at the last moment, you can fall straight down without hitting the sides.

Fast Fall