I had similar questions and figured them out by myself and though this is now super late I figured I would post here in case you are still wondering or someone else wanders in and is wondering the same.

First of all the forward backflip thing you see in all the good runs is done by

1. Hold forward
2. press and ¤hold¤ the secondary attack (default as right mouse click)
3. press the dodge/backflip button any time before the end of the animation to flip forward. The real trick is that the fastest part of the movement is from the dash so ideally you want to start by turning your character around so that you dash in the direction you are intending, then as soon as you are facing the right way start your dash and wait until right as the dash ends and you start the attack portion of the animation to back flip so that you can maximize distance while spending as little time as possible standing still This is probably the hardest part to get the hang of for speedrunning but not too bad once you know how to actually do it.

Stage 1 When you clip into the wall from the moving platform you simply need to step off the platform toward the wall at the right time, getting the exact time can be a bit tricky but just watch some runs to get a feel for the timing.

Boss fight After breaking the crystal and freeing her immediately spam towards her and jump around her in a circle so that the crystals don't spread apart. The trick to doing the first part efficiently is to jump in circles around the crystal until the witch shoots her attack, then take a few shots on the grouped crystals before repeating. Getting hit by the skeletons or crystals attack will only cause minor stun lock and knock back while getting hit by the witches attack will push you far back and cause the crystals to fly out to their staircase positions at which point when you try to group them together they will be in the normal triangle position making it nearly impossible to hit multiple at once let alone all three.

I think all other tricks are fairly self explanatory as they are mainly just lining up jumps and either dashing to a lower level or doing the forwards back flip trick in the right situation. If you have any more questions about a specific trick/clip/thingy then ask and I'll hopefully see it and know how to answer it =p.

I wish the forums had some sort of notifications for when people post so I could reply sooner :) But yeah, Greenmittenz pretty much covered everything, one thing to note is that you have to be holding forward to dodge forward, just holding right click and pressing dodge will still send you backwards, but you can dodge forward while standing still as long as you are already holding right click and holding down 'w' (or whatever key you have set to walk forward, this is pretty useful in stage 4).

The main thing to note is, don't be put off if you can't do the skips! You can still get a time under 20 minutes without all the fancy tricks, and honestly, trying to get the first clip will put you in a constant loop of resets. Fortunately, most of the skips after the first 2 levels are fairly easy.

I look forward to seeing your runs!