TLDR. I cannot get “Eterna-lly Yours” to unlock.
Others . . .
“d is for…” and “eternally yours” are not unlocking, I’ve had Eterna on from the moment of entering the realm, way over 5 minutes, and a stock Ford Mustang '65 (pi 499) ticks the first two boxes when pinned but not the last one
hm, a not-stock VW Beetle worked for the speed one
I assume it makes no difference but “Danse Macabre” was playing when that unlocked!
I pinned the accolade in my first visit when it didn’t work, left it there while changing car and went back in, though that would be a bit daft if that’s a requirement
these were both free mode
skill mode didn’t unlock the music one, went in listening to eterna and that’s fixed at 5 minutes so should have worked in terms of time
3 2 1 Go in the Stadium Track is also bugged, it doesn’t start the 10 seconds or even register when you go over the 75mph.
Also pretty sure the 100 speed skills in free mode achievement is bugged for me, plus the drive a car from every decade one popped before I’d done a 30’s and 20’s car.
Yep, can’t get “D is For…”
The answer to that accolade might be “dumb design decisions”
All Accolades worked for me - I have them all unlocked.
But I played most (all?) of them in Free Mode. For sure the “Radio” ones.
I am still working on the Achievements.
Playing on XSX.
I tried quite a few D class cars and the stock Toyota Sprinter ended up working for me
How’d you get the Time-Wyrm accolade to complete?
Maintain a speed of 88mph for 1 min? tried a few cars both tuned and stock and hasnt completed for me
You mentioned in the main Horizon area, and I followed up there and mentioning here, that the free roam skills achievements appear to require banking chains for the skills to count.
I also had Spanning Generations pop early, though after I had gotten into a 1930s car but before a 1920s car. I started with a 2020s car, then 1960s for the Dodge Charger accolade, then I switched to another 2020s car for something, then went decade by decade from the 2010s, though not doing the 1960s again. Was saving the Halo Warthog for last, just in case.
don’t suppose you remember anything about the one for listening to Eterna at Día de Muertos?
done multiple times in free mode and twice in skill mode, nothing
sadly my gut feeling on this is it’ll be added to the known issues list and . . . cue tumbleweed . . .
I successfully used the stock (=untuned) 2021 Lynk & Co 03+ (the yellow car from Autoshow) for both - the Time-Wyrm and the Shooting Star Accolade - directly after each other in one session without braking.
In Free Mode I was driving inside the stadium on the outmost full ring (but still inside!).
Playing on XSX.
You are lucky because of course I remember:
I successfully used the stock (=untuned) 1992 Volkswagen Golf GTI 16V MK2 (the red car from Autoshow) for the three - the Eterna-lly Yours, the Under the Petals and the D is for Accolades - directly after each other in one session.
In Free Mode I was first shooting the photograph, seconds later starting from the arch I did the speeding accolade. Directly after this accolade showed I braked on the spot and left the car standing for five minutes until the radio accolade showed - completely standing still - controller untouched.
I tested that you even could go into the game menu during the five minutes - the accolade timer will not be restarted. It just continues after you are again in the game.
I did not pin any of the accolades (all Horizon Realms). I do not know if that made any difference.
Sorry to hear that you are having problems with the new accolades!
Playing on XSX.
For me, the game also failed to register “Time-Wyrm” as complete in Accolade form while the achievement version popped up properly 
And I got the accolade, but not the achievement “You Might Need a Map”
EDIT: I got “Time-Wyrm” and “3, 2, 1… Go!” while driving an Extreme E car (#6) while “D is for…” unlocked immediately after I entered Día de Muertos in the stock Beetle, didn’t even have to move an inch 
I swear, those speed-related challenges and accolades are so weirdly selective…
Oh, and for “You Might Need a Map” achievement, for whatever reason, I had to drive around the maze a little longer than for the accolade 
Didn’t have to bank “drift, drift, drift” skills for it to count as I spent a good solid 20 minutes in lunar drift, for drift taps (and losing skill chains). Still popped around that time.
…but thanks for the tip. I’ll bank my speed and wreckage skills in free mode. Although I do have quite a few banked already. Only two I have left.
Switched from a D class Titan to the classic mini within free mode and that worked right away despite the Titan not working.
With the achievement for the 32 km this at first was the same as you described it: The accolade popped - the achievement did not.
Luckily I later drove on because of something else and after some more kilometers the achievement popped as well. Obviously the achievemend is bugged and needs some more kilometers. I can only estimate but something between 5-10 kilometers more.
Playing on XSX.
Update: I now successfully managed to get ALL Horizon Realms Accolades AND Achievements.
Bugged from my own experience are all Free Mode Skill achievements which require banking. This is no Forza Horizon standard behaviour and is confusing.
As already described the You Might Need a Map Achievement is bugged because it requires far more than 20 miles to drive.
Add to that the issues when chosing a car which - according to the Accolade requirements - is correct but the game is not accepting it. Just out of pure luck I avoided that but I have no doubt that these issues - as several of you described them here - are existing.
Additionally against Xbox standards is that all the new Horizon Realms Achievements do not show progress. This needs to be fixed as well.
Playing on XSX.
thanks for the info, I’ll look at it later - makes me wonder, if the counter doesn’t stop, maybe I went in, left, was outside with the counter ticking and it went over 5 minutes so it’s never going to get completed . . .
