Sorry I haven't had a chance to deal with this yet.
In short:
1-1: GCTK24 manages to OOB by restarting at the very beginning but I have never gotten it to work and may have got patched out.
1-2: You will see from my run that I am not good at this one. You have to jump on the cyrstal to the left, on to the boxes and then pull towards the camera to breach the invisible top of the barrier. GCTK24's run is a better example of how to do it.
2-1: This is a hard skip and I don't even try it, best to look at GCTK24's run for an example. I think the key seems to be the second jump and timing the movement left but I could never work out how to do it (I managed it just once from my recollection).
2-3: There is a skip by bumping into the mob near the beginning, as below. I do not use it as (a) it is inconsistent and (b) it drops 2 chests (or 3?).
4-2: You will see in my run that on the third crushing block in that level I position myself on the edge of where the block will land, and when it lands it propels me into the stratosphere. As soon as that happens I steer up and slightly left until it seems I am over the mountain, and when the camera shifts to under the crushing block near the end (looking up) I nudge up a little and mash the hit button until eventually I come falling back to ground and (hopefully) the end of the level.
I think those are the only known ones atm but I think there are lots more to be found. in particular, the super jumping (as per 2-3 and 4-2 mentioned above) can work on a lot of mobs / blocks but I have not tested out what other skips are possible using it. The only problem is the minimum chest count required to progress into new areas / the final boss, so any chests you skip using OOB you must get somewhere else instead.
