I would love to see how you did it

Harika

Umm... I kinda feel that grace jumping after a dash is like a ground jump because the reason why you can do that is because I think it still considers your on the ground. Though that's why I decided to reroute the whole thing but now grace jumping after a dash is a jump (also I think it should be called beating the game in blank amount of ground jumps and not jumps since there's jump in wall jump but oh well). Since you can't grace jump out of a dash anymore, what you can do is wall jump of the floor instead of ground jumping of the ground like this which is what like what Parchment did in 500m. Most of the time this is the solution:

If you can't wall jump of the floor you can just dash. Since I can't spam this whole posts with my GIFs, I skipped showing levels that either is the same to what Parchment did (400m) or levels that can easily be routed using the method of just wall jumping of the floor. I will also add GIFs of levels that can be way easier than Parchment showed. I will just add text descriptions for some levels if they are easy to explain in words. A few more other things to note a spike's hitbox is smaller than it looks (900m and 1500m) and you can actually be quick enough to wall jump off a breakable block you stepped on (1000m and 2800m)...

In order: 200m, 300m, 500m, 600m, (For 700m, just do it normally but dash instead of jump no need to cloud jump), (For 1100m, you can wall jump of the breakable block, get to the higher place to wall jump then stall for the cloud like in 600m), 1500m, 1900m (No need to spike clip), 2400m, 2700m

Sorry if there is so much GIFs... For this run, you need 6 jumps. One in 1100m when jumping off the cloud in the most left side where you don't have much height by just jumping, one in1300m when reaching for the first balloon, one in 1700m, the same situation with Parchment, one in 1800m jumping from the cloud to the balloon or the floor to the balloon, one in 2300m and one in 2600m when jumping up above the spikes since you don't have enough height. It was fun routing all of this. Obviously you need more jumps but hey... 

Since I found this challenge fun I decided to do the strawberries also.

1 Jumps in 400m (Use Speedrun Strats)

3 Jumps in 700m (Use the regained dash from the berry so you won't have to jump again off the cloud)

1 Jumps in 1400m (Use spike clip)

Here are some ways to avoid jumping in Old Site and 1300m (I did a spike clip there like what Parchment did though no need to change polarity):

Also while routing this, I found another way to do 1500m:

what is grace jumping? did i missed something?

Ik this is an old post, but I wanted to show this, the closest I've gotten to removing the 1 jump. I've tried many, many methods, but this one is the closest that I've found. (and, hilariously, the easiest lol)

Also wanted to show this alternate method to 1900 M, if spikejumps are too hard for anyone.

A little bit of an update post. The game is actually possible to beat with no jumps under these rules. (2 if spike jumps are illegal)

I explain this in a different comment, but basically wait until the strawberry in 1700 is at its lowest, fall into it, timing it such that you can dash up and collect it in the same frame. You will get another dash, so dash up again, spike jump, then its a success.

Edit: You can dash-jump instead of spike jumping