Via excessive Steam API magic and brute trial and error, I've established the following:
0. There's a lot of contradictory information about this achievement on the web. Since FP got updated a lot of times in the meantime, it's quite probable that the exact requirements for this changed a bit over time. Still, as of Jan 2023', the following rules apply. Some things here are really confusing, so I'm not blaming anyone here, but people get mistaken really easily here, see below for the most common caveats.
1. The "we haven't crossed the line" in the outro is not directly related to this achievement - i.e. you can get it and don't get the Golden Path Achievement.
2. For the sake of it, go for it at Easy difficulty - no HoP and high-level hope/discontent management and some crucial high-risk-high-reward abilities make doing it on higher difficulties a chore. Also, it solves some dillemas mentioned in 8. below.
3. Most of the Adaptation laws are OK by themselves (see 6. below), including some non-obvious ones like (all have been tested as 100% OK):
- Soup (Adaptation Law), including extensive use
- Moonshine (Adaptation Law) (including Public House (Adaptation Law), including extensive use)
- Extended Shift (Adaptation Law) (including extensive use and Emergency Shift (Adaptation Law), but not the Emergency Shift Ability!)
- Organic Fertiliser (Adaptation Law) (including Organ Transplants (Adaptation Law) & Corpse Disposal (Adaptation Law)) (using Utilise the Dead Ability wasn't tested due to lack of suitable test subjects :D)
- Overcrowding (Adaptation Law) & Prosthetics (Adaptation Law), including extensive use
- Duelling Law (Adaptation Law) (extensive use not tested, might be problematic)
- Triage (Adaptation Law) (the Triage Ability itself is forbidden, so no real reason to take it though!)
4. House of Pleasure (Adaptation Law) is forbidden (i.e. it blocks this achievement completely). I haven't tested Child Labour - Safe Jobs (Adaptation Law) etc. or Radical Treatment (Adaptation Law) myself (EDIT: Confirmed, Radical treatment does not block the achievement), but I believe they might be OK also - still, there's no real reason to take them, especially on Easy or when trying to get this achievement. I'd assume that only HoP is forbidden as far as Adaptation tree goes (but would still mind the caveats).
5. If you're playing Order, Prison (Purpose Law) and Propaganda Centre (Purpose Law) are both forbidden. (don't believe people saying Prison is OK - maybe it was at some point, but as of 2022 it is not, see 0. above); extensive use of both Patrol and Foreman Ability are OK.
6. If you're playing Faith, at least Faith Keepers (Purpose Law) are forbidden. I haven't tested it, but from what I gathered most probably Righteous Denunciation (Purpose Law) is prohibited also. The Temple (Purpose Law), House of Healing (Purpose Law) and Field Kitchens (Purpose Law) are explicitly tested OK, at least as the laws themselves.
7. As a general rule, the law being OK doesn't make the ability OK (and vice versa, just because the ability is forbidden doesn't make the law forbidden). Using Emergency Shift Ability is forbidden at least on buildings (I haven't tested it on piles because I had none left, but you can assume it applies as well - if you're playing on Easy you won't need it anyway); the same applies to Triage Ability, although the law itself is OK (though it makes no sense to select it and take the Disco/Hope hit when you can't use the ability itself). In general, some laws might trigger some events that break this achievement, but since they are random and time-based, I couldn't test them all explicitly.
8. A lot of people mention stuff like Londoners, Crises, deaths etc. Honestly, based on what I've seen myself, I believe they are mostly unrelated to this achievement. I had the usual day-1-houses-please crisis and it made no difference, I could still get the achievement. I've read numerous people having lots of crises and getting it. I don't see why other crises should matter for this one. As for the deaths, there are numerous reports of people having different deaths (from events, from not discovering people on map in time etc.) and still getting the achievement. Some deaths are forbidden though, but mostly they are results of e.g. applying a forbidden ability (e.g. Triage or Emergency Shift). I'm too lazy to hard-verify it myself (I've already spent more than I wanted on this), but I'd assume that the deaths by themselves aren't the problem, it's the decisions/abilities/laws that are here. 26.03.2023 edit: Letting your people deal with thieves is OK.
9. Feel free to add any additional info that's missing above. I've wasted more than enough time on it already :D
14.03.2023 edit: I can confirm that you can not use Child Labour - Safe Jobs (Adaptation Law). Also the biggest change that made me get this achievement is putting all Healthbuilding in the same area (close to the cookhouses in best case). People are stupid and straight up move to the Healthbuilding that is already in use instead of going to the closest one - they also might go to eat before treatment and die on the way to treatment (that only matters if you try the achievment in higher diffcultys i guess). That is especially a problem when the refugees arrive.
26.03.2023 edit: Medic/Engineer Apprentices (Adaptation Law) is OK.
2024-05-10 edit, by different editor: With Order, the scripted death of the guard chasing thieves is OK. Child Shelters are NOT required (but I also didn't put them to labor - I just never signed either law). Getting stomped on by an Automaton and refusing to slow them down is also OK.