It's not necessary to kill in exactly 1 blow, you just need to deal the exact amount of damage once. No "overkill" as it might be termed in another game. Any damage you do above and beyond what is necessary to beat the stage becomes the stage's remaining health.
So if the stage has 3 hp remaining and then you do an attack that does 10 damage, the stage will be left with 7 hp. If you then do 10 damage again, the stage will be left with 3 hp again.

There's a fair amount of discussion and strategy talked about in this thread, but as far as I'm aware no one has actually completed it. Everyone gets frustrated and gives up.

This challenge is extremely difficult and tedious if not outright impossible at the moment.

Basic tricks and gotchas and warnings if you want to try it:

• This is a constant struggle between wanting to do tons of damage in order to get the levels done faster, and wanting to do little damage so that you can do the exact amount of damage needed to finish the level. Ideally you want to be able to swap back and forth between them without getting locked into one or the other, but most of the stuff in this game are permanent increases, locked in for an entire run, or permanent increases within a run.
  
• Find some combination of cubes that can do 1 more damage than a different combination of cubes.
  
• You probably have lots of multipliers that don't add up to whole numbers. This can cause your cubes to do seemingly inconsistent amounts of damage (i.e. 1 white = 2 damage, 2 white = 4 damage, 3 white = 7 damage, 2 blue = 8 damage).
  
• You can use the overkill penalty to your advantage. If you know how to do "10" damage and "3" damage but the stage has "7" hp left, then you can do 10 damage and the stage will be left with 3 hp, and then you can do 3 damage.
  
  • Order matters: If you 10 damage then 3 damage, you win. If you do 3 damage then 10 damage, then you will need to do another 6 damage.
    
    • |7 - 10| = 3. |3 - 3| = 0
      
    • |7 - 3| = 4. |4 - 10| = 6.
• Prestige skills are not permanent. You can unselect prestige skills in order to do less damage.
  
  • Definitely unselect any Attack +% skills
    
  • Keep Auto Collect / Auto Attack.
    
  • Unselect as many other skills as possible, as each skill increases your "skill sphere multiplier" by 10 percentage points.
    
  • The prestige skills that make the white cube randomly become other colors is very awkward. Nice for speed, but really frustrating if you've just burned down almost all of the hp, only to get a gold cube to show up unexpectedly and do a trillion hp of overkill.
    
  • You probably want to have the Power of Cube enabled, but you don't want to use it unless you get stuck (i.e. have an odd amount of HP left, but all of your cubes only do even amounts of damage). In which case you should probably slot in some white cubes in order to increase your Power of Cube multiplier by 1%, then immediately unslot the cubes.
    
  • Booster skills are hit or miss. They might ruin your perfectly timed click of the Attack or Collect button. Or they might break you out of a loop by getting your white cube to fire slightly earlier than normal.
    
  • Samurai helper is good for burning down whatever levels it can do damage to without doing overkill. And you can control when the samurai is equipped or not. But the upgraded form is a trap.
• Prestige Tier 5 has a skill called "Collect Bonus Attack + 10%", which lets you deal 10% of your Collect as damage, effectively letting you cut your damage by a lot if you want. But in exchange you give up the ability to do "0" damage.
  
• A lot of the challenges give you permanent bonuses that make this harder.
  
  • The "Zoom Multiplier" from the "Broken Meter" challenge can become massive (I'm currently getting my damage multiplied by 45 times just by this) and you can't turn it off.
    
  • The -0.1% HP from the Titanium cube challenge can make the level have annoying amounts of hp that aren't convenient to work with. Might be good to repeat that challenge until it at least adds up to a -0.5% or -1%
    
  • The Normal and Only White Cube challenges increase your "Challenge Bonus Multiplier" which can't be turned off.
• Be very careful about upgrading your ticker speeds. You don't want them so fast that you can't react fast enough to them

I actually did it when I tried it again.

What I did was unselect boosters and white -> color prestige skill. Didn't bother taking off other multipliers.
I don't have enough skill point to even reach the collect:attack skill, but I wouldn't take it if I could.
For tick speeds, only got 1 level on white to 1.87 seconds. Kept every other at their base speed. Allows better breathing room for 2 whites. 3 whites is impossible. But I think You should aim to base your late game on 2 white -> 2 single whites cycles. 1 more level and faster speed on white might be better, didn't try. Will try on my next 4 attempts to 5/5 it.
Use power of cube on whites to adjust damage.

In my case, I didn't have to use the power of cube until Phase 6-10.
If I remember right, had no real trouble getting to phase 9 with green. But then found out my damage was way too low for it. Also had too weak of a magician and no helper. So had grind a few days just to unlock orange. Also had to get some blue power of cube multiplier(not the blue upgrade costing blue blocks) to boost damage, kept white low to more easily fine tune damage later. Otherwise, it would have easily taken over a week just for this part.
Then I got to part 10 and had to grind until I could buy upgrade on magician unlocking platinum.

Then came the gruesome part of the end since I had to up my damage that was now 335/671. The lowest I managed to bring it down was in the 120s. So about 120 cycle of timing 2 whites and 2 single whites. Took a small break every now and then to not make any mistakes due to carelessness. You really have to watch out for all those other cubes.
And I did end up doing a mistake with a white + orange. Thankfully, I noticed what it was and simply did the same combination again and recovered.

For my next attempts, unlocked another helper equipment slot by doing robot challenge and got helper helper. Magician and helper are currently 249 and 190.
This will make it VERY much easier and faster since I likely won't have to boost my damage as much and still be able to bring phase 9 and 10 down.

I abused my knowledge of computer science to guess this might happen, and was rewarded with this stupidly easy cheat (assuming you are already doing tons of damage):
If you do an absolutely massive amount of damage with an upgraded samurai (optionally with helper helper assisting), the game forgets about whatever tiny amount of HP the level actually has when setting the phase's hp. Then the second hit of the samurai perfectly clears the level. So you can do the entire challenge in ~30s. I managed to get my extra Update slot before I even left the Helper menu.

Currently I achieve this with my Samurai doing:
29.4 Novg damage base
50.4 Tg damage with Helper helper

The 29.4 Novg damage is sufficient for doing this trick, no Helper helper required.

I could have sworn I had done this before in frustration, so I'm not sure if it was a newly introduced bug or if I just hadn't sat around long enough. Unfortunately 29.4 Novg damage is the lowest I can currently get so I can't say how much you actually need to abuse this.

Got my achievement and finished all 5/5 challenges and the measly +5% attack multiplier.

I'm now prevented from attempting this challenge anymore so I won't be able to help out further / test anything.

For anyone that hasn't actually gotten far enough to see "Novg" as a unit, that is 10^90, and "Tg" is 10^93.

If I had to guess, you can probably do this once whatever amount of damage you can do is at least the level's HP * 2^32 or level's HP * 2^64 or 2^128, since the trick here is doing so much damage that the game ends up forgetting about the tiny amount of difference between "2.94 * 10^90" and "(2.94 * 10^90) - (relatively tiny number)",
10^90 is approximately 2^299, which is many many orders of magnitude away from the 2*10^20 (~2^67) HP that phase 10 has.

Originally posted by Primalmoon:

For anyone that hasn't actually gotten far enough to see "Novg" as a unit, that is 10^90, and "Tg" is 10^93.

If I had to guess, you can probably do this once whatever amount of damage you can do is at least the level's HP * 2^32 or level's HP * 2^64 or 2^128, since the trick here is doing so much damage that the game ends up forgetting about the tiny amount of difference between "2.94 * 10^90" and "(2.94 * 10^90) - (relatively tiny number)",
10^90 is approximately 2^299, which is many many orders of magnitude away from the 2*10^20 (~2^67) HP that phase 10 has.

Thanks for that strategy and explaining how this level actually works! That was really helpful! I passed it the same way.

I can tell you that at least at Max Damage 278Sp is too little to pass P8 with this trick. Samurai is doing 4.18Oc damage with my Helper Helper, so its gotta be higher than that.

Originally posted by ♥♥♥♥♥♥♥♥:

Thanks for that strategy and explaining how this level actually works! That was really helpful! I passed it the same way.

Glad someone else was able to use this.

Originally posted by byah Arl1x:

I can tell you that at least at Max Damage 278Sp is too little to pass P8 with this trick. Samurai is doing 4.18Oc damage with my Helper Helper, so its gotta be higher than that.

Yeah, I wouldn't expect it to work that early, at least not for phase 10.
4.18 Oc = 4.18 * 10^27 ~= 2^91

That's still short of being 2^32 * 2^67 for phase 10.

Did it work for any of the earlier phases? (phase 1 through 9?)
2^91 is definitely much bigger than the 5, 20, and 50 hp of the first few phases so if the threshold is HP*2^32 or HP*2^64 then you would have been doing it for those levels.

---

For anyone looking at this and trying to figure out how to do these calculations and can't quite remember how to do that, you want to use the change of base formula to figure it out.

log(your damage) / log(2) = some power
That "some power" is what you need to raise 2 to in order to get your damage.
2^(some power) = your damage

---

Assuming I was right about the boundaries, around these are the damage numbers you should be testing out:

• 32 bit differences: 2^67 * 2^32 = 2^99 = 6.33 * 10^29 = 633 Oc
  
• 64 bit differences: 2^67 * 2^64 = 2^131 = 2.7 * 10^39 = 2.7 Dd
  
• 128 bit differences: 2^67 * 2^128 = 2^195 = 5 * 10^58 = 50 Od

Exact number is probably off though since there was some rounding but it should be near those.

Originally posted by Primalmoon:

for any of the earlier phases? (phase 1 through 9?)

Yes, it works for all earlier phases. Currently at 68.5No damage with my Samurai + Helper and it craps out at Phase 10, not quite enough there. Back to grinding higher!

Just found the answer, it's 1Ud. It takes a Samurai 1Ud of damage to clear Phase 10.

Another way (also utilizing Primalmoon's method explanation) I used was whittle down the boss HP until it was around the e8 range and then jump in helper helper + samurai. Kind of tedious my way, but if your samurai isn't at the 1Ud range of damage yet, it may be an option.

Originally posted by byah Arl1x:

Just found the answer, it's 1Ud. It takes a Samurai 1Ud of damage to clear Phase 10.

Perfect, thanks for that.

Ok, if it's 1 Ud then that means I had the right idea, but my boundaries were off because I was thinking of integer data types instead of floating point data types. In retrospect that's my bad. This game has to do a ton of floating point math with all of its multipliers, so it makes sense that it would use them here.

I think the exact number you needed was ~1.3 Ud, since that's 2^120, which ends up working very nicely:

• 1.3 Ud = 1.3*10^36 = 2^120 = 2^67 * 2^53

That makes it a 53 bit difference, which is significant because that's the amount of significant bits that can be stored in a standard "double".
https://en.wikipedia.org/wiki/Significand#Significands_and_the_hidden_bit

Originally posted by wikipedia:

For example, the same IEEE 754 double-precision format is commonly described as having either a 53-bit significand, including the hidden bit, or a 52-bit significand, excluding the hidden bit.

So that must be what the game is using under the hood.

With that we can be fairly confident that you must be able to do "Current HP * 2^53" or more in one hit for this trick to work.

Originally posted by Thanatos:

Another way (also utilizing Primalmoon's method explanation) I used was whittle down the boss HP until it was around the e8 range and then jump in helper helper + samurai. Kind of tedious my way, but if your samurai isn't at the 1Ud range of damage yet, it may be an option.

Neat. We can incorporate that with this learning about 2^53.
If you want to figure out how much you need to whittle the level down to before the trick can work, take the amount of damage your Samurai can do and divide by 2^53.

Since that math is a bit annoying to do, here are some example values that people can reference.

If your Samurai can do:

• 1 Ud
  • the level needs to be under: 10^20 = 100 Qi
• 100 Dc
  • the level needs to be under: 10^19 = 10 Qi
• 10 Dc
  • the level needs to be under: 10^18 = 1 Qi
• 1 Dc
  • the level needs to be under: 10^17 = 100 Qa
• 100 No
  • the level needs to be under: 10^16 = 10 Qa
• 10 No
  • the level needs to be under: 10^15 = 1 Qa

Originally posted by Primalmoon:

Originally posted by Thanatos:

Another way (also utilizing Primalmoon's method explanation) I used was whittle down the boss HP until it was around the e8 range and then jump in helper helper + samurai. Kind of tedious my way, but if your samurai isn't at the 1Ud range of damage yet, it may be an option.

Since that math is a bit annoying to do, here are some example values that people can reference.

If your Samurai can do:

• 1 Ud
  • the level needs to be under: 10^20 = 100 Qi
• 100 D
  • the level needs to be under: 10^19 = 10 Qi
• 10 D
  • the level needs to be under: 10^18 = 1 Qi
• 1 D
  • the level needs to be under: 10^17 = 100 Qa
• 100 No
  • the level needs to be under: 10^16 = 10 Qa
• 10 No
  • the level needs to be under: 10^15 = 1 Qa

Thank you for those numbers, they def are good reference points!