Intro

First of all, a warning: if you’re aiming to get the all medals achievements, think it twice. The Asura Medal has the prerequisite of getting S rank on ALL STAGES(excluding DLC and El Shaddai). If you’re willing to go through that Japanese torture, I wish you luck.

Extra notes:
-(G): golden medals are worth 3 points. S rank requires 15.
-You can see a list of your medals in: pause menu > archives > medals.

List

-Time Medal 1(G): Finish within 40 minutes.
-Time Medal 2(G): Finish within 30 minutes.
-Time Medal 3(G): Finish within 20 minutes.

-Survival Medal 1(G): Finish with less than 100 total damage.
-Survival Medal 2(G): Finish with less than 50 total damage.
-Survival Medal 3(G): Finish with no damage.

-Covert Medal 1(G): Finish with no more than 2 Apparition detections.
-Covert Medal 2(G): Finish with no more than 1 Apparition detections.
-Covert Medal 3(G): Finish with no Apparition detections, and no sounds heard. (If your screen flashes like a TV static, you’ve already failed at this medal).

-Great Cremation Medal(G): bury more than 2 Apparitions.(Bury means to kill/cremate in this context).
-Escape Medal: Successfully run from an Apparition.
-Cremation Medal: Cremate an Apparition.
-Trap Medal: Drop an Apparition into a hole.
-Slapstick Medal: Chased around by an Apparition more than 3 times.
-Barrier Medal: Enclose an Apparition in a barrier.

-Guidance Medal: Get an Apparition to break an enforced door.(enforced door = locked door).
-Intruder Medal: Destroy an enforced door yourself.
-Unlocker Medal: Unlock 3 or more locked doors.

-Crybaby Medal: Steal a magatama without being discovered by a Shion.
-Parasite Medal: Steal a magatama from a cocoon(caterpillar baby) and escape.
-Next Medal: Recover a magatama while taking no damage from inside a swarm of Human Cocoon Moth.(Seems to be bugged and you get it even if you do take damage).
-Scream Medal: Recover a Magatama without being noticed by a Hanged Man.(easiest with a black feather)

-Soul Sender: Release the souls of 10 or more corpses.
-Binge Shopper: Spend 2500 or more souls at Hotaruya’s shop.
-Light Medal: Light more than 20 fixed light sources.
-Darkness Medal: Finish without lighting any fixed light sources.

-Gunman Medal: Stop an Apparition 3 or more times with a ’26 Pistol.
-Exterminator Medal: Drive away an insect 3 or more times.
-Exorcist Medal: Drive away 3 or more Impure.

-Warp Medal: Warp 2 or more times.
-Spacetime Medal: Stop time 2 or more times.
-Item Medal: use 9 or more consumable items.
-Heavy User Medal: Consume 1 or more passive items.
-Minimalist Medal: Finish without getting any items(not including Compass, Archives, Coffee Beans).
-Glutton Medal: Eat 5 or more Oni Giri.

-Ice Medal: Get a brain freeze after eating something cold.(Eat in close succession 3 of the popsicles you can find in Hydrangea Street).
-Mystery Medal: Operate a mechanism using Souls.
-Resurrection Medal: Kindle a Light of Life.
-Briber Medal: Finish with Bribery Equipped.(buy the card from Yakumo. Make sure it is not sealed when you clear the level)

-Traveler Medal: Finish having traversed 3 km or more. (In Archives > Records you can see your total distance walked, so if you want you can take a note of it when starting a level).
-Shortest Distance Medal: Finish having traversed 1 km or less.
-Heart of Darkness Medal: Increase your Trauma. (Must be done in advanced difficulty or above: lock Trauma in a barrier and after 30 seconds a new one will spawn at the exit.)

-Moustache Medal: Finish with a Moustache Dandy equipped.(Unlocked by talking with Yakumo after purchasing all the karuta.)
-(G)Asura Medal: Finish with Shacles of Asura equipped. (Unlocked after clearing ALL STAGES with an S rank or higher).
-Cheat Medal: Finish with a powerful karuta equipped.(Nullifies score and prevents unlocking achievements, but additional medals obtained do count for your collection).

That’s it

I had to search though a lot of Japanese and Chinese pages to find out the requisites for some of the medals I was missing, and at such a time I wished there was a list of the medals on Steam, so I decided to be a kind soul and do it myself.
Good luck getting this achievement, you’re really gonna need it.