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These achievements are "in-game" achievements only (that is, they are not Steam achievements).
However, they can increase your Damage Per Second (DPS) rate in the game, so they are well worth getting.

* Click 12 times per second.
Reward: Increase damage per click by 1.

* Click 14 times per second.
Reward: Increase damage per click by 3.

* Click 25 times per second.
Reward: Increase DPS by 3%.

* Click 35 times per second.
Reward: Increase DPS by 5%.

To get the highest clicks per second, try the following five steps:

1) Hit "Lens of darkness" (the 8th skill box) - this skill will enable the doubling of the next skill you click on.


2) Hit "Flurry of blows" (the 1st skill box) to get 10 clicks per second (CPS) - which, with the effect of "Lens of darkness", is thus doubled to 20 CPS.


3) Hit "Mad Hatter's clocks" (the 9th/last skill box) to decrease the cooldown time of the last skill used (which will make the "Flurry of blows" skill available once again).


4) Hit "Flurry of blows" (the 1st skill box) again (which should add another 10 clicks per second - which should thus bring the total up to 30 CPS).


5) Click as fast as you can to get the remaining clicks per second.



As a further option, you could hold off doing steps 1 to 5 until you get a fly (i.e. the insect which sometimes flies across the top of the game screen); click on it to trigger a random skill - and if you are lucky enough to get the "Flurry of blows" skill, then do steps 1 to 5 (which should bring the total number of clicks per second up to 40).

CPS resets
The "clicks per second" unachieved achievements (i.e. those which you have not attained as yet) will reset when you close the game.
However, that doesn't matter, because they are not cumulative achievements.
The achievements you have already attained are not affected by this.

Auto-clickers
Auto-clickers is an option that some people may use.
However, as far as I am concerned, it is cheating or at least untoward behaviour against the spirit of fair gaming - therefore, I have not included any "how to" information on that subject here (I've never used one myself, but their use seems to be quite rife amongst gamers).

Is the CPS counter working properly in this game?
As a test, I brought up the achievements section in-game and watched the percentage increase when the skill boxes were hit.
However, I found that the first 4 steps would achieve no more than 20 CPS - which would make it seem that steps 3 and 4 won't count towards the total.
If the skills were cumulative, they should get you up to 30 CPS, and then you would only need to do 5 CPS to get the total up to 35 clicks per second.
However, I have done all of the above - and so far it has only got me up to 25 clicks per second.

I have tested myself in-game (watching the percentage increase in the achievements section in-game) and it seems that I can only go as high as 10 CPS manually (although I'm pretty sure I've done better than that in other games).
Using steps 1 and 2 got me to 20 CPS straight away, but even when I madly click away the game's CPS counter only goes as high as 25 CPS - which seems to be a dubious count (even if it will only register in 5 click bunches).
Therefore, I have to wonder if the game is malfunctioning or somewhat broken.

Anyway, have a go at it.
You should at least get the achievements for 12, 14, and 25 clicks per second.
Fingers crossed that you get the 35 clicks per second achievement as well.