Here is the full list of all 42 Zero IDLE achievements. It takes around 15-20 hours to unlock all of the achievements on Windows.
Don't click background for 1 hour of active playing
Prestige for the first time
Earn a billion coins and become a member of the elite club
Earn one hundred thousand coins
Click background 999 times
Click background 300 times
Click background 10 times
Click background 9 times within one second
Click background 20 times within one second
Log In Zero IDLE via Steam
Start the game
Finish the game
Earn billion coins again after prestige
Click background 10000 times
Earn 1 Quadrillion coins
Earn 1 Sextillion coins
Earn 1 Octillion coins
Earn 1 Decillion coins
Earn 1 Duodecillion coins
Earn 1 Sexvigintillion coins
Buy 8500 generators
Earn 60 achievements
Buy 3000 generators
Buy 150 upgrades
Consume Your First Essence And Start Making Your Tree Bigger (More Big)
Consume 15 essences
Play this evolution for 1 day
Consume "Bills And Gates"
Prestige without crystals to gain
Prestige 10 times in a row with 0 earned coins
Prestige 100 times in a row with 0 earned coins
Prestige 666 times
Gain +60,000% mult from the "Melony", and then go idle (no clicks for 60 secs)
Click background for 10 minutes STRAIGHT (ok just click once in less than a minute for 10 minutes and you're fine)
Synthesize your first Thymine
Synthesize your first Adenine
Synthesize your first Guanine
Synthesize your first Cytosine
Synthesize 46 nucleotides
Gain 7e20 (700 Qi) Crystals
Have any two generators one of which is 7th level and the other one is 0th
Don't click background for 6 hours of active playing