Some people on Youtube said this should have been a guide on Steam, so here you are. ^_^
The new (well, it's fairly old now) Nexus feels more like an advance manouvre test than a skill test, but I admit I had a lot of fun trying to solve the puzzles.
In the first video you can find how to reach all doors.

At 2:50 I use a technique called "spike jump" (with it you can jump on 45° spikes as long as you dash down and keep pressing the jump button), if you don't want to use the move you can reach the door the proper way as showed in the second video.

A couple of quick tips:

- You can press dash then jump near a platform edge and you'll be executing a perfect last second jump
- You can dash straight away from a wall without losing the ability to do an air jump
- You can press jump when sliding down a near-vertical wall to a vertical wall the very same moment the wall slope changes to execute an extended run up the wall
- You can keep pressing up to run on ceilings, even when they're made of angled slopes
- If you jump, dash down and land on a slope few inches away from when it reverts to flat you can dash toward the flat portion and gain a tremendous speed, gaining a lot of height if the flat surface leads to a trampoline shaped structure

Hope these help.
Good luck and never give up on this fantastic game (up to Yotta, at least XD ).