Seeing as there still isnt a solution to this yet, I decided to add something like a live journal of my own ongoing journey of getting this achievement. In order to get info on this I either had to directly message people for advice or check Steam forums from the PC version, so hopefully this can be a more concise and helpful version for TA people.
Warhammer 40K Inq has a morality system, where at certain story moments you have to make choices that lead to one event or another. The achievement needs you to reach the maximum value for Puritan choices or Radical, which is 300. You cannot directly see your morality score as a numerical value, but if you go to the morality chart certain skills you can unlock have numbers stating what morality rank they are, so you can get a rough guess where you are at at any given time. You cannot accumulate Radical and Puritan points simultaneously, your choices exist on a horizontal line axis, and moves left and right based on your decision. This means for example if you are going for Puritan and are at 150 Puritan value and accidentally choose Radical, your Puritan value will decrease by 20 (i think), so youd have a new value of 130 Puritan.
How to get Morality points
There are only 2 current ways of getting morality points, Story decision, and Priority Assignments (will explain these in a bit).
-Story Choices: As of completing the story missions through the second season DLC (Khorne), I had 220 Puritan. I am pretty sure I always choose puritan choices, so this seems to be the maximum you can get from current story missions. I assume that all the decisions regardless of morality choice are the same value, so if you choose Radical each time I'd guess youd be at 220 Radical as well. But larger point... 220 is currently the max you can get from story.
-Priority Assignments: This is the only other way to get morality, and it is incredible annoying because it is largely random number generated. In your home base area, there is a guy in the upper right who allows you to do Priority Assignments. These are little mini story arc missions, that can be anywhere from 1-4 missions to complete. Sometime when starting these missions, a choice you can make will have a radical/puritan choice attached, which is where you get these morality points.
So let me put down a few key points before i describe my current status grinding these priority assignments.
-The number of priority assignments you can do at any given time is limited. You accrue 1 priority assignment a day, and can only hold a maximum of 3 at any given time. These accrue automatically, and you just simply have to wait for them to replenish.
-When you start a priority assignment, you will always be met with an opening decision. Afterwards you might have anywhere between 1-2 more decisions after that. The morality choice ONLY occurs on the first decision menu. If you don't see one there, you aren't getting one for that priority assignment.
-The likely hood of a puritan or radical decision is the same regardless of which one you are going for, 100% random number generation.
-The amounts from my experience have always been +15. (the number is stated next to the decision)
-The morality points seem to apply to you as soon as you make your decision. I do not believe you have to play the actual priority assignment. I personally always played just because I was nervous about wasting a morality choice if I was wrong, and also because blasphemers must be purged for the Emperor's glory.
My Process for unlocking (still ongoing)
The best way to unlock this is to START EARLY. This game normally takes a lot of grinding just to get through the campaign and other achievements, so don't be an idiot like me and not do priority assignments until the very end. The slowly accruing counter of priority assignments makes this a brutal slog if you haven't been doing it early on. But once you start trying to grind these, below are my following steps.
1.) Wait 3 days till I have 3 priority assignments saved up
2.) Start an assignment
3.) If the first choice shows a Puritan (or radical depending on what you want) choice, AWESOME! one step closer. Select it, and then choose whatever other choices you want after. As noted above, I would always finish the priority assignment by actually playing the missions. But I think you are good to go to step 4 at this point (if I am wrong, very sorry)
4.) If you do not get a morality choice in your first menu (or if you did and dont want to play the mission). Hurry through the other random choices, and then start the mission.
5.) As soon as the missions starts. Hit start, and surrender.
6.) Most of the time, this will end the priority assignment completely, and you will get a 'Finish Assignment' screen. Sometimes the priority assignment wont be over, and it will require you to start a 2nd mission. Just quit that one the same way as before.
7.) Start a new priority assignment, and try again!
Thats the best I can do for you, the random nature of these choices makes this really annoying. I started off getting 3 puritan choices in 5 assignments... and then i went 3 weeks without getting another one. You will also be getting random choices for the WRONG direction at times also, which makes this even more annoying. Below is a tally (for other's reference as well as my own tracking) about how often I am getting missions. You might get it way faster than this, or even take longer, but im putting this here for reference.
And with that... good luck. Ill add more updates as I get closer, or if I run into other issues.
Priority Assignments Started: 41
Puritan Choices : 6
Radical Choices: 7
% of missions with any morality choice: 32%
% of missions with my chosen morality: 14%