This is a pretty easy achievement but in my case I had some "buggy" problems that may have simply been stupidity on my part. ~see further down
To submit a prayer you need a "light of rebellion". You have a chance to earn a "light of rebellion" by earning the ranking of investigator at the end of a match. To get the ranking of investigator:
-According to wiki sources "You have to have around 10 pieces of bonus evidence collected during a match."
-Crash righteous said he got one level 3 with 3/7 pieces of evidence.
-In my experience, they are more rare the higher your level.
If you earn a "light of rebellion" it will show up after a match near the exit door/map selection of the train inside a case. Even though the entire team earns the investigator ranking, not all players will receive it; it is random.
Once you have a "light of rebellion" use it immediately. If something should go wrong you have to be ready for another chance at getting another one before reaching level 20. Plus, you can only have one in your inventory and they expire after 5 days. Use the item in your own lobby in case the host quits.
Head to the back of the train car to the sleeping area. Approach the mirror and select the "light of rebellion" not sacrifice body[-i] . Make sure that you have "ultimate horror experience" selected via option/audio. Then, step back into the circle and hold . Keep holding until the achievement pops; it should take about 30-60 seconds. I used the headset microphone.
CAUTION If more than 2 minutes go by and no achievement, power off your XBOX as releasing will create an undeletable save state.
My buggy experience:
First attempt showed the word "listening" but was not centered; "listening" was split at the top and bottom of screen. Second attempt I tried on a second account that I used to boost the score multiplier was done on a different council. Third attempt I deleted local save and it showed no word listening; powered off. Forth attempt and working final; deleted the local save but this time plugged in a headset to the controller.
In all cases, the update news banner was on the screen and did talk while attempting this each time.
Finding Bonus Evidence
Hopefully, you won't need this next section because everything went well for you.
In order to get at least ten bonus pieces of evidence, choose a mission that has at least 19+ pieces available. When you start a mission, look for the instructions like "hide the evidence/destroy the evidence/clean the evidence." You may have to quit a few matches before coming across this. make the world dance is another good option too but wont appear until the end of a mission
Now go to a private match and make sure you have stalker off. Go out and find evidence while taking note of all the locations. When you fail, simply restart the mission and MOST of the evidence will be in the same location. The objective and sub-objective evidence will move a little and the blood spots that you clean up will move and vary in number too. The cleanable blood spot are usually placed between the two evidence locations and the photographable sub-objective evidence will move too. This mission should earn you about 5 pieces of evidence.
Bonus Evidence Locations[-b]
Here is a link to a map and a collection of photos.
Generally speaking I NEVER found any evidence in bathrooms in houses, on top of house roofs, on top of vans, in closets
I usually found found one at the bottom of the map near the Hoadly's Leap sign either under the bench or on the tree. The treehouse was fairly consistent with a spawn but requires a grappling hook.
The instrument supply is always a reliable start if you know the possible spawn locations. Host Conditioning and Dream Therapy both have one possible spawn location each but they rarely spawn so I would concentrate efforts elsewhere.