A general trick I figured out is that you can go through many things that block the way.
I did that by standing in front of them then turn around without moving back and turn around again.
Repeating this method you can go closer to the enemies or objects until you can go through them.
I discovered that trick in Level 3 while jumping into the dog. It is very easy to skip the dog because you only need to do the method once after you jumped into him.

This run has four hard parts :

1. Jumping between the big monkey and the sign triggering both at the same time in Level 1.
2. Getting through the closed door while stealing the key in Level 4.
3. The ghost skip trick in Level 8, because it needs a good timing
3. The jump after the rails go downhill and suddenly there's a hole in the railway in Level 10.

The rest of the run is pretty easy, here are a few comments to the single levels.

Level 1 : After skipping the guy who was blocking the door, you can actually jump over that sign and don't have to read the help text.
Level 2 : Good run, but 59 seconds is possible.
Level 3 : Failed at grabbing the toilet paper while running through the house.
Level 4 : Fail while going up the stairs on my way to bomb the first wall.
Level 5 : Very good time, my all time best is a second faster but the time depends on the plants movements.
Level 6 : Failed at the first attempt to jump to the door with the bomb.
Level 7 : Good run, could be a bit faster at the last chains of light by jumping at the one right before the very long chain. I was worried to fall in the pit so I didn't jump at this one.
Level 8 : When getting back with the pillow to the key room the ghosts slowed me down a bit.
Level 9 : Fail at the beginning of getting the last bone up to the bomb.
Level 10 : Very good run, no fails.
Level 11 : With the right timing of jumping and helicopter mode it is possible to jump from the garbage bin to the platform over it.
I failed while trying to do this so I walked the normal way to not loose more seconds.
I found out that you can skip the money task too, it is about 7 seconds faster to not steal the safe first
Level 12 : Failed at the third bomb by going away from the boss platform too early, he was still calling enemies and didn't recognize me.
You can't jump over these enemies if they block the way to the bomb, luckily that happened only once.

All in all I am very happy with that record.