This guide is done and you can get 100% with it, but some achievements could need more information, so help is much appreciated. :)
I will also mention that you helped or even add you as a contributor. :)

Dogmatic



Possible on 1st and 2nd Invocation. (You have to get it to get to 3rd Invocation)
Easiest one to get. Just take the option to sign the contract on the ritual night.

Not on my watch




Possible on 1st and 2nd Invocation. (You have to get it to get to 3rd Invocation)
This one is a bit harder and can easily be missed, because it needs some work.
Ps: It is needed to progress in the story though.

The first thing you have to do, is to leave the crowbar there on night two.
On the next night you will find the crowbar again.
Use it on the pile of rocks to get in the room behind it.
There you can now open the locker and can take a memory card.
On night four you have to gather the gun and the ammunition for it.
On the ritual night you have to insert this memory card into the computer.
The last thing to do, is to take the option to use the gun.

Purple Skies



This one you will be able to get on 3rd Invocation.

The first thing to do is to look at the locker in your room.
Ps: It doesn't matter if you do it on your normal apartment or in your apartment, which is connected with the one from the professor and Emily, because you need to do this to progress.
The next thing you will do get the key from the other locker in the connected apartment area.
The next thing is to use this key on the ritual night to get to the sewers.
After you solved the sewer puzzle, you will be able to use a seperate way.
The last thing to do, is use the portal and go with Mr. Crane.

Nonconformist



Pretty easy: just finish the 4th Invocation.

The patient



Pretty easy: You will get it close to the beginning of Meeting, it doesn't matter which option you'll take.

Who is Riley?



Easiest done on 1st Invocation, because it seems like you'll always get to that location there.
If you want to do it on other Invocations (only on the 2nd possible I assume) then you just have to read the diary everyday and after the knocking on the door in the connected apartment area, go through the southern door. (If that isn't 100% right, tell me)
So after some time you'll get into an area, where you find a man in a cell and Ben says that he maybe can help him.
Now your goal is to solve every puzzle in this area, the order doesn't matter.

Warning: If the creature in the basement gets you three times, you'll be forced out of the area.

Chain puzzle:

Warning: If you fail, you'll be set to the start of the area and if this happens to often you'll be forced out of the area and back to the connected apartments.

This is pretty easy, just open the padlocks in the right order.
Solution: Graduate,Accident,Enlightment,Ambition,Relocation,Gatherer,Intervention,Megalomania,Drown


Computer puzzle:

First thing you have to do, is getting the USB from the basement.

After that you just have to take the three right files from the computers and put the stick in the last one.
Solution:8th March 1957, 2:12pm, Thought 3


Dark room puzzle:

This is pretty much way forward.
Get the lamp from the basement.
Plug it in.
Open the crack in the wall.


























Hidden room puzzle:

That's an easy one too.
First get the abacus from the basement.
Warning: Don't try to get it with a lamp, diploma or USB in your hand, because you won't be able to take it and will never be able to again in this playthrough. You can take the diploma and USB after taking the abacus though.
Ps: I already posted this bug in the discussions.
After that go into the hidden room and place the abacus on the table there.
Now just wait for the person to take it and leaving the room.


























After you completed all above puzzles, you can now go into the cell and after the scene and being back in the connected apartments, you'll get the achievement.

Who is Emily?



This is at least doable on 1st , 2nd and 3rd Invocation. Dunno about 4th Invocation, if somebody knows, tell me.
For this sidestory, you have to do following things every day:

Eat something
Clean up your plate
Water the plant

After you have done it everyday, you should get to the sidestory after the connected apartment area aka. before the ritual night.

The Company



For this achievement you have to collect all company token.
Please note: If you found a token already, it won't appear a second time.

First Token:Floppy Disk

Easiest done on 1st Invocation, because you'll get to this area.

After you lit up the area, the first thing is to fill the left sink with water.
Then go to the right sink and you'll drain the sink.
Now go back to the first sink to get a key.
With this key you can open the closed cupboard.
Now you check the hole in the wall.
~Image follows, forgot to take one~
After that you'll be able to get a broom from the cupboard.
Now use it on the hole and you'll get the first token.


























Second Token: Timecard

This should be doable in the 1st Invocation, but I didn't found it there and didn't want to reset the game a third time for it. That's why now screens for the 2nd/3rd Invocation follow. If you want to do it on the 1st Invocation, just look for the mentioned things in the area.

This is pretty simple, but very easy missable. On the ritual nights, after you grabbed the idol, some mannequins will appear.
After a few steps towards your goal, you'll hear a sound of something that shattered.
At this point you have to move the mannequins with the light, until you are able to get to the far left. There you'll find a mirror that fell over and there you'll find the second token.
Ps: For the 1st Invocation just search for the shattered mirror. (If somebody got screens from it, tell me)


























Third Token: Medicine

As you can already tell from the s creen, it's very easy. After the medicine cabinet has appeared, just look at it and you'll get the third token.

Fourth Token:Key Card

This is pretty easy as well. On the third night of the 4th Invocation after you'll be able to move objects, just move the oven and you'll get the fourth and last token.

The Nameless City



For this achievement look through every possible window (at day and night!) on one Invocation.
After that look through every possible window on another Invocation and you should get it.
The reason is that after you watched through every possible window in one Invocation a second set of messages will be triggered.

Regular



For this achievement you have to check your pc on every occation (read every mail and board) on both sets of mails/boardresponses. If you do that right on 1st and 2nd invocation, you should get the achievement while playing the 2nd invocation.
Ps: If you think you missed something in the 1st Invocation, just go with the 3rd Invocation, because it has the same set of board messages.

Scatttered Knowledge



For this achievement you have to get full Solution Lore on every Invocation.
Just interact with every possible item you can find and you should get it easily.
If you miss something just replay the Invocation later and look at everything without advancing the story first.

1st Invocation: 0 Solution Lore
2nd Invocation: 5 Solution Lore
3rd Invocation: 9 Solution Lore
4th Invocation: 8 Solution Lore

You might need a prefix



This is possible in every Invocation that starts with a box appearing in your apartment. Just after you fixed the light user your phone to dial 5676.

I wrote that story



This is only possible in the 1st Invocation and there for you have to complete the tablet puzzle to open the safe on night three on the first try. Solution: Departure, Deprivation, Sin, Regret

Where he started



I'm not 100% sure about that for now, but I'm pretty sure you first have to do the requirements to get to Riley (aka. the same as for the achievement "Who is Riley?"), but before you go into Riley's cell, you have to get the diploma.
Ps: I never had the diploma otherwise with me, that's why I'm unsure about it.
After the talk with Riley, you are back in the connected apartments. There just go the empty frame and insert the diploma.

A feast for the prince



In the ritual night there is a fridge locked with a number pad. You have to first look at it to find the note with the code. Or if you are lazy you can just enter the code 4923 now.
After that you have to look twice at a box in the upper left of the apartment to get the code.
After that you can enter the code into the fridge and after Ben talked about what is inside the fridge you'll get the achievement.

A bastion of calm



This only worked on 3rd Invocation for me.
First thing you do, is try to call Molly after you examined the box.
On the second day you'll be able to call her.
After that you have to call her a third time on day three.
And finally on "night" four, after you picked up the idol, the phone will ring and after the conversation you'll get the achievement.

A short detour



This has to be done on the 4th Invocation on the third night.
You get to the point, where you have to find another way. The first thing you do is check the jeans to get a key.
After you are able to move and search objects, search the trash to get some matches.
After that go to the locker and search it and you should be able to investigate the hole and after you did that you have the achievement.

Strange locked book



You will get this after you got every other achievement on the same save file. (aka. not reseting the save file and getting everything)